Arsenal survived a late Everton rally to leave Goodison Park with a 2-1 victory and the three points.
The Toffees should have taken an early lead when Seamus Coleman raced away from Gael Clichy and sent in a cross that Tim Cahill, uncharacteristically, headed off target.
Andrey Arshavin twice fired wide as the Gunners grew into the game, but they went ahead in the 36th minute when Tim Howard blocked a Samir Nasri effort only for Arshavin to tee up Bacary Sagna to fire home.
It took only three minutes of the second half for Arsenal to double their advantage as Denilson and Marouane Chamakh combined to create an opening for Cesc Fabregas to score with a cool finish.
Everton responded well and Jack Rodwell shot agonisingly wide, but the Gunners were looking dangerous on the break and Chamakh somehow lifted a shot over the bar from six yards with the goal at his mercy.
At the other end Jermaine Beckford, who rescued a point in midweek, forced a superb diving save from Lukasz Fabianski, and the Gunners goalkeeper then saved well from Steven Pienaar and Louis Saha.
He could do nothing about Cahill’s goal with a minute remaining in normal time, but Everton could not find a late equaliser for the second time in five days.