Against Bayer Leverkusen—a club currently four points ahead of Borussia Dortmund in second place in the Bundesliga—the reigning English champions have done the double, winning 4-2 and 5-0 at home and away respectively.
Group A minnows Real Sociedad surprisingly offered more resistance, securing their only point of this year's campaign against United in Spain.
Moyes' team won their home game with an early away goal yet struggled to add to their total against the Basques even with Shinji Kagawa carving up chances left, right and centre.
Now, having already made sure that they are mathematically certain they will be one of the two teams to progress from Group A, United must face Shakhtar Donetsk at home in order to decide who will finish top.
The two clubs drew 1-1 in Ukraine on Match Day 2 in October and a win or another draw would make sure that United claim first place and the more favourable draw in the round of 16.
But how will United line up in this crunch fixture against the South American flair and Eastern European foundations of Shakhtar at Old Trafford?
Hit the button below or click the arrows above as we consider Moyes' options and potential team selection for the sixth and final Match Day of the Champions League group stage 2013.
With Wayne Rooney set to return to the team after serving a one match ban in domestic competitions, Robin van Persie may well be relegated to the bench having looked half fit against Newcastle United at the weekend.
The Dutchman has struggled with a number of niggling injuries of late and Moyes may want to rest him to ensure he doesn't face anymore down time as United's season continues to list as Christmas approaches.
Michael Carrick remains at the care of the physio team and therefore unavailable for selection.
Shakhtar have no first team injury problems to report.
Mircea Lucescu's visitors—who have won the Ukrainian Premier League seven times in the last nine seasons, as well as lifting the UEFA Cup in 2009 and five Ukrainian Cups—are an accomplished and well-equipped outfit who will fancy themselves to claim all three points at Old Trafford.
Four of those league titles have come in the last four consecutive seasons and while the squad may have had to endure a major remodelling in the summer, they are now once again looking like a force to be reckoned with.
Their recent form reads as four wins out of four in all competitions with striker Luiz Adriano having scored three in his last three games. Moyes' team are without a win in their last four games and have been without their own key forward, van Persie, due to injury.
In Shakhtar's last Champions League game in Group A they smashed Real Sociedad 4-0 at the Donbass Arena in Donetsk—a display that put United's own efforts against the Spaniards at home decidedly in the shade.
Having watched Fernandinho leave for Manchester City, Henrikh Mkhitaryan head to Dortmund and Raznan Rat depart for West Ham on a free, Lucescu had initially been cautious in promoting the likes of Bernard and Fernando, but his new imports have begun to find their feet.
As United fans will remember from the 1-1 draw in October, such players add a touch of South American sparkle to Shakhtar's defensive backbone of Croatian attacking right-back Darijo Srna and Ukrainian international defenders Viacheslav Shevchuk, Oleksandr Kucher and Yaroslav Rakitskiy.
At the heart of Lucescu's favoured 4-2-3-1 formation, the midfield pivot tends to feature a duo that typifies this blend with the likes of Taras Stepanenko or the Czech Republic's Tomas Hubschman and Fred or Fernando.
European discipline, hard work and tactical nous augmented with the Brazilians' flair for creative improvisation and individual skill, linking up with their attacking midfield stars Douglas Costa, Alex Teixeira, Taison and the like.
The well-rounded chemistry of this multi-national combination was almost too much for Moyes' team in Ukraine, and United must approach Shakhtar's visit with caution and a plan if they are to draw or win at home on Match Day 6.
Goalkeeper: David De Gea
The former Atletico Madrid shot stopper has become an assured presence between the sticks for United, yet appears under no illusions that, in general, standards have slipped of late.
David De Gea: "We're falling off the pace. The team isn't playing well, especially at home."— La Liga Action (@LaLigaAction) December 8, 2013
Hopefully his own excellent form and ability to pop up with incredible saves can act as an example to inspire those higher up the pitch to raise their game this season, starting with their match against Shakhtar.
Central Defence: Chris Smalling, Jonny Evans
Rio Ferdinand openly criticised Moyes' methods regarding match preparation this week, as reported by The Guardian's Jamie Jackson on Twitter:
Ferdinand tells BT Sport Moyes' selection policy can make him feel like "a madman" as don't know if playing until close to kick-off #mufc— jamie jackson (@GuardianJamieJ) December 6, 2013
Such candor may see him lose his place in United's Champions League team, having featured in three of their five European games so far.
Fortunately, with Smalling in good form following his appearances at right-back, Moyes can turn to the younger English centre-back to partner Evans at the back.
The pair should be a well-balanced mix of competency on the ball, decent physicality, aerial power and mobility, well suited to facing down Shakhtar's fusion football.
Full-backs: Patrice Evra, Rafael
Much will be required of United's full-backs however, with the like of Costa and Taison set to resume their relentless quest to dribble and drive at De Gea's goal as they did in the October match.
With Smalling a potential replacement for the dissenting Ferdinand, Rafael could be handed a start at right-back, with the Brazilian needing to convince a rather fickle Moyes of his defensive qualities as well as his attacking potency.
Evra has so far been able to hold his new manager's confidence, but that may be due to a lack of other options at left-back.
His position remains under threat however, with Moyes still likely to seek competition if not an outright replacement for the Frenchman in January.
Shakhtar represent a valuable opportunity for both Rafael and Evra to prove themselves once more before the new year as United seek to ensure they finish in first place in Group A.
Central midfield: Phil Jones, Ryan Giggs
Jones returned to the United midfield against Newcastle but found himself paired with Tom Cleverley rather than the 40-year-old who had shredded Leverkusen apart from deep: Giggs.
With Carrick out, the veteran Welshman was forced to play against Everton and so therefore unable to feature against the Magpies due to tiredness.
However, it's likely the young prodigy and the old master could well line up together again in Europe against Shakhtar, with Giggs' experience and Jones' energy set to be tested against the Ukrainians' combo of Eastern Europe and Latin America.
Moyes knows he's onto a good thing with United's Champions League form this year, and is unlikely to want to mess too much with a formula that was so ruthless in Germany against Leverkusen.
Attacking Midfield: Antonio Valencia, Shinji Kagawa, Nani
Valencia and Nani were subbed on and off for Adnan Januzaj and Wilfried Zaha respectively against Newcastle, meaning that the two wide men who tore Leverkusen to shreds will be fairly fresh to face Shakhtar.
Although the Portuguese has struggled for regular games, he looks to have rediscovered some of his finest form of late, and was lively against the Geordies even if United failed to win at the weekend without scoring a goal.
This follows on from some impressive defensive work against Leverkusen, which will come in handy against the Ukrainians' attackers and Darijo Srna down the left.
Man Utd have made 6 interceptions in Leverkusen's half, all of them coming down the left flank. Nani & Evra in form. pic.twitter.com/YXTNqahb6F— Squawka Football (@Squawka) November 27, 2013
Similarly, Valencia was ever-present down the right flank against the Germans, and his work rate will be vital in combatting any threats down his flank.
Meanwhile, assuming Kagawa is well enough to play after having his stomach pumped due to overeating, as per George Ankers of Goal.com, he too should start after a number of impressive, even if statistically insignificant, performances in the Champions League this season.
While the Japanese playmaker is yet to record a goal or assist this season he has produced 10 key passes in as many games according to WhoScored.com, highlighting his ability to create the opportunities that lead to assists, if not the assists themselves.
Striker: Wayne Rooney
Ahead of United's attacking midfield three will be Rooney, who looks set to be brought straight back into the team after serving his domestic suspension.
The striker-cum-box-to-box-midfielder has been in fine form this season with 10 goals and eight assists from 17 games so far, per WhoScored.com, with two of those strikes and three of his assists coming in his four Champions League appearances.
Having agitated for a move out of Old Trafford in the summer, the former Everton youth star now looks to be United's de facto saviour, and Moyes will be looking for Rooney to run the game from the front, and link up with Kagawa and co.
It's unlikely chances will come easy against Shakhtar however, and the Englishman must be ready to snatch whatever opportunities he is presented with.
That would mean that United's line up against Shakhtar at home on Tuesday, December 10 would consist of the following personnel:
GK: De Gea
DF: Rafael, Smalling, Evans, Evra
CM: Jones, Giggs
AM: Valencia, Kagawa, Nani
A draw would be enough for United to top the group, but as Moyes is hopefully learning, playing for a stalemate can be a recipe for disaster or at least complacency with a team more used to taking the game to their opponents.
If he sets his team out to try and get at Shakhtar rather than purely react to their plans, he could once again walk away from a Champions League fixture at his new club with a handsome result.
Shakhtar will be determined to get a result of sorts with the prize of first place a possibility should they beat United and Leverkusen breathing down their necks for second place should they lose or draw.
The Germans face bottom-placed Sociedad on Match Day 6 and are likely to grab a big win against the Spaniards, meaning that Lucescu's cannot take anything for granted.
It's hard to understand Moyes' working at present, with the ex-Everton manager at times appearing to be trapped within the damage limitation mentality his successor on Merseyside diagnosed as the club's ailment prior to their 1-0 win over United, as per The Guardian's Andy Hunter.
So often United have blossomed in the Champions League this year before withering away to nothing again in the Premier League. Is Moyes making a conscious decision to play a fluid game in Europe and a cagey, conservative and rather comprised and rigid set-up in England? If so, it's so far proven to be a deeply flawed strategy determined to fight a war on two fronts that doesn't exist.
Evans believes the team has struggled through a crisis of confidence, as reported by BBC Sport:
The lads have lost a bit of confidence. You can tell that with the possession and creativity. Players maybe are not playing how they naturally would. That happens when your confidence drops.
United's lack of belief is likely to have many causes, not least Moyes' at times confusing approach to man management and morale boosting.
Previously this season he has publicly criticised his players—an anathema to Sir Alex's reign where the team was backed at all times—suggesting to the press that his squad lacks quality, as per Simon Mullock at the Mirror, and his reportedly unpopular training methods according to Wayne Vasey of Goal.com.
As reported by Phil McNulty of BBC Sport, following his side's devastating 4-1 defeat to City back in September, Moyes could barely hide his open frustrations with those on the pitch as he questioned their application.
Yet the manager himself has come out and declared that United's season is far from dead due to "the players—because I am working with the champions," again as reported by BBC Sport.
Perhaps then he needs to learn how to make them feel like champions before he can rely on them to play for him as they did for Ferguson—a proven winner whose reputation preceded him.
Until he can inspire his players with comparable silverware, Moyes must come up with a clear vision and identity for his United era to match the skills, intelligence and ambitions of his stars.