The hosts―who left top scorer Luis Suarez on the bench for all but the last 14 minutes―were out of sorts for much of the first half, with frustration the main emotion emerging from a capacity Anfield crowd who were expecting a comfortable victory.
The breakthrough was finally achieved when Iago Aspas calmly stroked home his first competitive goal for the Reds after being found in the penalty area by Raheem Sterling nine minutes into the second half.
Stand-in home goalkeeper Brad Jones made a fine save from Michael Petrasso to keep the scoreline at 1-0, and with Suarez now on the pitch, the Reds grabbed a second when Sterling's wayward drive was turned into the opposing net by defender James Tarkowski.
There was time for a romantic FA Cup moment as Oldham's Anton Rodgers came off the bench to face the team managed by his father Brendan, but ultimately it was to be Liverpool's day despite the brave efforts of their visitors.
Here are six lessons learned from the game:
Living in the rather large shadow cast by Luis Suarez must be pretty tough, and especially if you've had injury problems too.
Both elements have combined to make the first six months on Merseyside particularly unhappy for Iago Aspas, who must have brought a smile to even the most cynical of observers with his well-taken goal in front of the Kop early in the second half.
Of course, the most romantic tale to have emerged from today would have been another Oldham victory over Liverpool following the 3-2 success in the fourth round last year, but ultimately the story was written by Aspas, who must use today as a starting point.
Liverpool's squad continues to look somewhat stretched and low on quality in some areas, especially when some of the fringe players deliver performances such as this.
One of the more telling issues of the day can be seen with the half-time withdrawals of both Victor Moses and Luis Alberto, players who must have looked upon today as a rare chance to impress in a match from the start. Both failed.
In fairness to Alberto, he at least looked interested in trying to make things happen and came close with a long-range effort, but for Moses this was just the latest in a series of frustrating displays that lead many to wonder just where his career is headed currently.
Unlikely to get back into the fold at Chelsea, he's now seeing his chances of securing a permanent switch to Liverpool slipping by the week.
Where he ends up next is up to him.
Whilst it is easy to bemoan the lack of quality within areas of the Liverpool squad, it is also only fair to underline that the Reds are spoilt for choice in some areas.
A fit and firing Martin Kelly would be a first-choice right-back for the majority of clubs in the Premier League, and it was good to see the Academy product back on top of his game and earning a start here as Glen Johnson was given the day off.
Indeed, there are some schools of thought which suggest that Johnson's performance levels have dipped somewhat whilst a new contract is being discussed, and so if ever there was a time for Kelly to impress, then it would be now.
Of course, any praised dished out from this game will be followed by the caveat of it being "only Oldham," but Kelly deserves to be pleased with himself.
If the 3-2 loss at Boundary Park almost a year ago is to be considered as the lowest point in Brendan Rodgers' Liverpool reign, then it is only right that we compare where the Reds are now to their state then.
There is no doubt that progress has been made at Anfield ever since that bleak Sunday last January, but Rodgers will still be concerned that a League One side―who contained only two players in the starting XI who started last year―were able to make life so difficult for his men until the own goal which killed them off late on. To put things another way, it is tough to imagine any of the other sides in the Premier League's Top 4 facing the sort of problems Liverpool did.
Of course, huge praise has to be given to the Latics side and their young manager Lee Johnson, who can be proud of their efforts and will no doubt be desperate to draw the Reds in the FA Cup for a fourth year in a row in 2015.
If matches against Oldham are to act as barometers for Liverpool's seasons, then right now the Reds' reads "can do better."
The good news is that they are in a pretty strong place from which to do that.
Considering that by limping off the pitch he left Liverpool with just 10 men at such a crucial stage of the game when they only led 1-0, it is safe to assume that Daniel Agger was in a fair amount of pain when he left the action.
Mamadou Sakho's injury means that the Reds' once vast amount of central defenders seems to be crumbling all around them at the moment, with only Kolo Toure left standing at full-time.
Should Agger be missing, it would be logical to expect Toure and Martin Skrtel to line up together when the Reds go to Stoke City next Sunday, and although both are experienced enough to deal with such a test, this constant chopping and changing of defensive partnerships is hardly encouraging at a time of the season when consistency is key.
With no European football and following an early Capital One Cup exit, the FA Cup has always been earmarked as a big tournament for Liverpool this season, and that belief is coming to fruition in more ways than one.
A fourth round tie against another lower-league team beckons, but with the likes of Manchester United, Tottenham and Newcastle already out of the competition, the potential for winning it has only grown.
In addition, Manchester City face an addition to their schedule with a replay that they'll have to fit in alongside other commitments, whilst Chelsea have a tough fourth-round tie against Stoke.
The FA Cup is looking crucial to their season.