Conversely, David Moyes' side slipped to just one spot off the bottom having now lost four out of five premiership games this season.
The visitors clearly had last season's 7-0 drubbing fresh in their memories and played deep from the outset. That said, the first effort on goal was from Marcus Bent who sent a 20-yard drive just wide of Jens Lehmann's right post.
Arsenal responded through Robert Pires, who saw a crisp shot deflected for a corner following a burst down the left flank.
It was the Gunners who opened the scoring after 11 minutes in un-typical fashion from a set-piece.
Jose Antonio Reyes clipped in a free-kick from the right flank and Sol Campbell rose highest to guide the ball beyond a stranded Nigel Martyn. The relief for the centre-back was evident from his reaction as he opened his arms and looked up to the heavens to celebrate.
The hosts then took control of the match and pinned Everton further and further back, as Reyes and Robin van Persie combined well to terrorise the Merseysiders.
One sweeping move saw Reyes find van Persie on the right side of the Everton area and his burst into the box should have lead to the Gunners doubling their lead.
But the Dutch marksman's shot hit the right upright, although referee Alan Wiley gave a corner, clearly believing Martyn got his fingertips to the shot.
Campbell proved his fitness when he claimed his and Arsenal's second on the half-hour mark.
The goal mirrored his first with Reyes clipping in another free-kick, this time from the left flank. As before, Campbell was rose unchallenged to pick his spot beyond Martyn.
Substitute Aleksandr Hleb showed his potential in the 38th minute with some intelligent play as he sold a dummy to the whole of the Everton rearguard, but it also appeared to have been to clever for his own colleagues as van Persie and Reyes got in each other's way in front of a vacant goal.
Even Kolo Toure felt he could afford to go on a 60-yard run two minutes before half-time, exchanging passes along the way with Fredrik Ljungberg, before seeing his audacious back flick bobble just wide of the left post.
Everton were clearly caught between strategies. They were fearful of pouring forward, but clearly needed to attack if they were to have a chance of getting something out of the game.
For the first 20 minutes after the interval Moyes' men continued to drop deep to deny Arsenal space in front of goal, which was successful in that it frustrated the Gunners, who seemed to run out of ideas.
As the clock ticked away Moyes threw on more attack-minded players, with Duncan Ferguson given the job of spearheading the attack, but to little avail.
Arsenal should have made it 3-0 after 70 minutes when Ljungberg seized on a parry from Martyn, but his overhead kick thundered back off the crossbar.