Thomas Vermaelen headed home a corner with eight minutes on the clock, an advantage Arsenal retained for the remainder of an enjoyable back-and-forth contest.
There was controversy later on in the first half, however, when Royston Drenthe had what appeared to be a legitimate equaliser ruled offside.
Nonetheless, the Toffees were unable to find a way back into the contest after that despite creating a number of chances, and remain in the top half of the table only via goal difference.
And with one of those teams just beneath them, Stoke City, holding Spurs to a 1-1 draw at White Hart Lane, Arsene Wenger’s side replaced their North London counterparts in the top three just one month after trailing them by 10 points.
Perhaps thriving in the knowledge that third place could be theirs by the end of the evening, the visitors raced out of the blocks and dominated the early stages.
A deft diagonal ball from Tomas Rosicky could and should have been headed at goal by Robin van Persie, only for the Dutch dynamo to play it selflessly at such a tight angle by nodding it back to an unmarked Aaron Ramsey.
The young Welshman inexplicably half-volleyed the gift over from close range, but the travelling fans were able to forget all about it just two minutes later.
A pinpoint corner from Van Persie on an otherwise off-night for the striker on the set-piece front was headed in by Vermaelen, who scored the Gunners’ last league goal to seal a late win against Newcastle nine days ago.
Both Van Persie and Ramsey were denied chances to double the advantage on the 10-minute mark by last-ditch defending and good goalkeeping from Tim Howard, before tactical manoeuvrings by David Moyes saw the hosts gradually creep back into the game.
With Marouane Fellaini moving alongside striker Nikica Jelavic and Tim Cahill dropping back to midfield, the Toffees began to see more of the ball and were denied an equaliser by a controversial offside decision around the half-hour mark.
Alex Song gave possession away in his own final third, allowing Fellaini to put Drenthe clean through with a great ball across the penalty area which inexplicably triggered the flag, despite the uninvolved Jelavic being the only man offside.
Keeping their heads up in hope of still finding a way back into the contest, the home side came out for the second half full of beans and roared on by their home support.
And though the assistant’s flag appeared to be auditioning for man-of-the-match honours with its frequent appearances and overbearing influence, Van Persie and Fellaini were nonetheless able to provoke gasps with their efforts either side of the hour mark. Van Persie hit the post while Fellaini forced a great parry from Wojciech Szczesny in the visiting goal.
As the final 20 minutes approached, the Gunners finally began to succeed in seeing the match out comfortably with Howard’s saves from Theo Walcott and Van Persie keeping the difference at just one goal.