I agree with sach. Arsenal got thoroughly outplayed and outmaneuvered tactically in the first half. They had no attacking width at all, so they were completely reliant on their fullbacks for width. Martinez countered by playing Mirallas and Lukaku as wide fowards pressed up high, which pinned Arsenal's fullbacks back. As a result, Everton's backline could stay very narrow when out of possession. Arsenal's strategy seems to have been to have Sanchez drag the CBs around and then play through balls to midfield runners coming from deep, but because Everton's defense was so narrow there were no gaps to play those balls, and when they tried them the Everton defense cut them out without much trouble. In the first half Arsenal created no real chances, had no attempts on target, and all five of their shots were blasts from distance by Ox.
They were even worse without the ball. Since there were no wingers in the side, and both of the nominally wide midfielders (Ozil and Ox) were always trying to come inside, there was no one assigned to track Everton's fullbacks. Both Coleman and Baines got forward repeatedly and created overloads on the wing. The midfield couldn't decide whether to press; a couple players would press while the others would sit back, and Everton would calmly form triangles and pass around them. Despite having a numerical advantage in midfield, no one was tracking Barry; he was 33/36 in passing in the first half and dictated the flow. All of this came together for the first goal, when from a free kick a Mirallas run occupied the fullback and opened up space for Baines on the wing, who then played a central ball to an unmarked Barry, who crossed to the opposite side to the unmarked Coleman bombing in.
Everton should have created even more chances, but Mirallas, while repeatedly getting into good positions, was poor on the ball (he had 6 take ons in the first half and lost the ball on all of them), and Chambers made a number of excellent last-ditch tackles and interceptions. The second goal was offside and shouldn't have stood but 2-0 wasn't an entirely unfair scoreline, Everton were the consistently more dangerous side.
In the second half, Everton tired and got more conservative playing with the lead. The fullbacks didn't get forward as much, and Mirallas and Lukaku ran out of gas and their threat declined. This, plus a greater agressiveness when playing from behind, allowed Arsenal's fullbacks to get forward, and it was only once they had width from the fullbacks that Arsenal looked at all threatening. Both Arsenal goals came from crosses from the left side in which Monreal's presence was critical; one was his cross, in the other his run helped create the space for Cazorla's cross.
The funny thing about the tactical battle is that Martinez played exactly the same way, with Lukaku wide instead of central to pin the fullback back, Naismith as a false 9, and the fullbacks getting forward to create wide overloads, in the game last Spring, to similarly successful effect. In that game, it was a surprise, since Everton hadn't played that way before. But Wenger should have been more prepared this time around.