A late headed goal by Nicklas Bendtner was enough to win all the points and keep alive their hopes of overtaking Avram Grant's side.
After a low-key start to the game, the first real shot of note came in the tenth minute from Arsenal's player of the month for April, Theo Walcott.
The youngster cut in from the left but his shot curled just wide of the right post.
Shortly after that Gilberto Silva met Bendtner's cute hoisted ball across the Everton penalty area, but the Brazilian could not stretch quite enough to guide his header towards goal.
It was Everton that came closest to opening the scoring on 28 minutes when Manuel Fernandes put through a delightful ball for Andrew Johnson to latch onto and his first-time shot was well-saved by the right boot of Lukasz Fabianski.
At the other end Emmanuel Adebayor got a toe to a couple of long ball over the top of the Everton defence, but nothing that overly troubled Tim Howard.
Gilberto again went close in the dying minutes of the first half when he rose unchallenged to meet a corner from the right, but he could not quite get over the ball so as to really test Howard.
Then, a minute later in to stoppage time, Adebayor should have made more or of Emmanuel Eboue's exquisite cross from the right, but only got a glancing connection with the ball and watched it fly agonisingly wide.
The second half began as slowly as the first with Joleon Lescott's shot being the only real chance on goal, and a half-chance at that.
While Everton did little to trouble the Gunners, they had more possession than their hosts which is a collector's item of a statistic.
Arsene Wenger tried to change things around on 70 minutes by getting Walcott to play on the right-hand side. He did that by bringing on Armand Traore as a left winger.
The tactic worked as the Gunners took the lead in the 77th minute. Bendtner found the young Frenchman with a slightly over-hit pass.
Traore got the ball under control quickly, burst down the left flank before delivering a perfectly flighted ball into the box that Bendtner powered home with a towering header.
Everton did not offer much of a response. David Moyes sent on Yakubu to try and bolster his attack, but to little avail. The Toffees' leading scorer was starved of any service as the Gunners went on to secure all the points.