Louis Saha had put the visitors ahead on 24 minutes when he slotted home, despite being clearly offside.
However, the Gunners turned the game around through substitute Andrey Arshavin and Laurent Koscielny's header.
The Gunners made some 10 changes from the side which had laboured to a 2-1 win over Huddersfield in the FA Cup here on Sunday.
And it was Everton - who have lost only six games, but find themselves in the lower half of the table because of some 12 draws - who started brightly.
With Diniyar Bilyaletdinov offering support to both Saha in attack and then making up the numbers in midfield, it was easy to see why David Moyes' men are hard to beat.
Arsenal midfielder Jack Wilshere was in the referee's book after just five minutes when he clattered through the back of Mikel Arteta, which would set a trend for the evening.
Everton continued to make all the running during the opening exchanges.
Arsenal finally got some passing together as Bacary Sagna was played in down the right, only to be chopped down by Sylvain Distin who was immediately shown a yellow card by Lee Mason.
Koscielny glanced a header through the six-yard box from a corner, before Cesc Fabregas then dragged a shot wide after a clever backheel from Robin van Persie.
The Gunners were now on top, but just lacked a decisive pass when in the final third.
Theo Walcott broke into the right side of the penalty area, but Tim Howard stood up well at the near post.
Everton, though, were ahead on 24 minutes in controversial fashion.
Saha was offside when Seamus Coleman chipped the ball through, but it spun off Koscielny's boot as he attempted to clear, falling to the Frenchman who slotted a low effort past Wojciech Szczesny.
Despite the protests of the Arsenal players, and consultation with his assistant Stephen Child on the far side, referee Mason allowed the goal to stand.
Arsenal felt more than a sense of injustice and centre-half Koscielny almost made amends when inches away from converting a corner with a diving header at the far post.
The frustration for the home fans continued after Fabregas burst into the Everton box only to drag his shot wide.
Van Persie then did brilliantly to collect a high, angled pass on his chest, but it would not drop and he could only loop the ball over.
Arsenal made a change at the restart, with Abou Diaby replacing Alex Song, who appeared to pick up an injury towards the end of the first half.
Rosicky spun away from his marker and charged forwards, but then dragged a 20-yard strike wide.
The home side continued to press, Diaby powering a header over the bar.
Arteta then went into the book after tripping Fabregas as the Arsenal captain set off on a quick break.
There was then a confrontation when van Persie went in on the Spaniard, and was also shown a yellow card by busy referee.
With 28 minutes left, Tomas Rosicky was replaced by Arshavin and Everton then sent Leon Osman on for Bilyaletdinov.
Diaby cut inside from the left and set himself, but then drilled his 20-yard shot wide.
Arsenal were finally level when Arshavin slotted home after Rodwell's backheader from Fabregas' chip fell to him in the six-yard box.
Osman tripped Walcott in full flow, and became the seventh man in Mason's notebook.
Van Persie sent the resulting free-kick towards the top right angle, which Howard did brilliantly to tip over.
Arsenal, though, were not to be denied and turned the game around when Koscielny headed home from the resulting corner on 75 minutes.
Rodwell glanced a header wide at the far post, but it was Arsenal who closed out the match and collected what could be three crucial points in the title race.