The three points were secured via a sublime solo goal from Kevin Mirallas, who briefly lit up an ordinary contest with a moment of genuine class.
Collecting a Tim Howard clearance well in his own half, Mirallas proceeded to sprint the length of the pitch, outwitting both Steven N'Zonzi and Geoff Cameron in the process, before slotting home past Asmir Begovic.
Both sides had decent chances to add to the scoring, but, almost justly, the Belgian's goal stood alone in defining the contest as the Toffees held on for their third Premier League win on the bounce.
Here's a look at some Everton-related talking points to emerge from this encounter.
Several hours before kickoff, Twitter became awash with rumours claiming Everton would be ditching their familiar 4-4-1-1 approach in favour of a vastly different 3-4-3 formation.
Many fans scoffed at this prospect, with several others sceptical, given how alien it would be to the side and how rigid manager David Moyes can often be with his defensive setup.
However, sure enough, as the game commenced, the Toffees were clearly deployed with three at the back and maintained that approach for the duration of the game.
John Heitinga, Phil Jagielka and Sylvain Distin anchored the side, with Leighton Baines and Seamus Coleman marauding forward from wing-back. Leon Osman and Darron Gibson continued in central midfield, with Victor Anichebe and Kevin Mirallas generally flanking Nikica Jelavic.
The mechanics of the setup meant Jagielka occupied the central defensive berth in possession, with Heitinga and Distin peeling out wide to hug the touchline. Osman and Gibson would then drop deep as Baines and Coleman advanced, while all three forwards interchanged with each other.
Certainly a new concept for fans to digest and something many would not have imagined from a Moyes selection.
So, did this unexpected change make a difference?
Despite the win, it's hard to be entirely swayed, as the game was decided by a moment of individual flair and Stoke are perhaps one of the least equipped sides to exploit a newly employed system.
Without two of their premier creative men, Marouane Fellaini and Steven Pienaar, Everton were still able to manufacture 13 chances, their exact average for games this season.
They enjoyed 54 percent possession, marginally above their season average of 53 percent, and recorded similarly unremarkable passes, shots and passing accuracy, all almost identical to a typical Everton game.
Therefore, it's hard to draw too much relevance into the system at all.
As the Toffees acclimatised to it, there were times it seemed to work well, especially in possession. With Stoke visibly stretched, Everton were able to play periods of the game at a much higher tempo, enjoying far more space in the middle to launch several attacks on the break.
Without the ball, it was perhaps less convincing, although Stoke's main threat was from crosses, where an extra defensive body became increasingly useful. Baines and Coleman were effective as wing-backs, but not as frequently involved in the final third, unable to exploit any two-on-one situations.
Overall, it's perhaps a system for Moyes to maintain and tinker with on the practise pitch, possibly implementing at specific occasions. It certainly suited the personnel deployed during this match and helped stifle the opposition, although a returning Fellaini may not fit so well in this system.
As mentioned, this game's major talking point was a stunning individual strike from Kevin Mirallas, which ultimately proved the difference.
With the Toffees missing Pienaar and Fellaini—two of their three most creative players who have fashioned out over 25 percent of their side's chances—the Belgian chose the perfect moment to take centre stage and shine.
In a contest that was always likely to be settled by a set piece or a moment of individual craft, Mirallas made his biggest contribution of the season and ensured his side collected the points with his goal.
As impressive as he was, it will be especially concerning to fans that he once again seemed troubled by a nagging leg injury as he left the pitch late on.
Considering Pienaar and Fellaini are still suspended for the Toffees' next crunch fixture at Tottenham, his presence will be imperative to his side.
One summer signing not quite enjoying the same adoration from supporters as Mirallas is Steven Naismith, who's struggled in his first season of Premier League football.
While the Scot is tactically disciplined, durable and occasionally clinical in the box, his is limited in several aspects of play, and Moyes' decision to exclude him from this lineup only highlighted his diminishing squad status.
With Fellaini and Pienaar out, the obvious decision was to call upon Nikica Jelavic and Naismith to fill the gaps in attack.
However, the fact Moyes completely altered his approach and then brought on Ross Barkley ahead of the Scot suggests the manager is becoming less convinced of his worth
After appearing for a solid 892 minutes in 2012, making nine starts and 10 substitute appearances at the club, Naismith has only featured for 299 minutes this year, starting three games and being called off the bench on just four occasions.
If he doesn't play with his side considerably depleted, it's hard to see where he figures in the Toffees' future.
After writing a piece suggesting Everton should consider moving on from Tim Howard, a sentiment not lost despite this performance, it's only fair to highlight an excellent return to the side from the American.
Many had questioned the wisdom of recalling Howard, given Jan Mucha's impressive recent performance against Manchester City. The Slovakian won many plaudits for that display, getting in the way of eight shots, more efforts than Howard has saved in any single match this season.
However, the American No. 1 more than justified his manager's faith, reacting well to smother two inviting chances, deflecting another effort wide and maintaining a notably commanding presence at most set pieces.
Everton have struggled with physical strikers and approaches all season, but—perhaps as a product of the new system—Howard and his defence generally seemed far more secure with an extra body present to fend off the danger.
After the volley of negativity aimed at the Toffees following a dismal FA Cup exit, David Moyes has done his best to galvanise his troops and prolong their domestic challenge for Europe.
Indeed, Everton are within reach of overhauling Moyes' record points tally at the club, with another 15 points required from the final eight games to eclipse the 65 points taken in 2007/08.
Given the fact Everton still have to travel to all of the contenders for Europe, that points haul would surely result in a European berth, something that the players, manager and supporters are all desperate to achieve.
There's no hiding from the challenge Everton face to achieve this, and the improbability that it eventually transpires. However, to still have a Champions League place in their own hands by the final few games of the season is an impressive feat.
As disappointing as the club's FA Cup showing was, Moyes and his squad must be commended for a generally high-class league campaign—their best for several seasons.
Next weekend's match at Tottenham is simply vital for the Toffees and will go a long way to define the club's immediate future. Win, and a good season could quickly become great.
Statistics via EPL Index