Arsenal shot out of the blocks with Theo Walcott again showing manager Arsene Wenger why he deserves a new contract by firing the Gooners ahead in the first minute.
Everton settled and the game became a more balanced affair before Marouane Fellaini, Everton's top goal scorer so far this season, fired in a low drive from outside the penalty area just before the half-hour mark.
The game ebbed and flowed with Everton creating the better chances: Nikica Jelavic smashed his shot over the bar after some great control, Steven Naismith missed a great chance in the area and a header from Sylvain Distin was well saved by Arsenal goalkeeper Wojciech Szczesny.
Arsenal looked a little toothless in all honesty, lacking that presence in the final third that now resides in Manchester.
Everton, who have only won one in their last eight games, could really use a win to kick on from their great start to the season and with Manchester City their next game up, the Blues could have done with three points.
The Blues do lie at sixth in the Premier League table though, and while the Arsenal game did not deliver in terms of points, the game did show some signs of life that Everton will be encouraged by.