Arsenal picked up from where they left off last season with a stylish victory.
Dennis Bergkamp marked the 500th League appearance of his career with a drilled shot, while a Jose Antonio Reyes header gave Arsenal a 2-0 half-time lead.
Thierry Henry's cross set up Fredrik Ljungberg for Arsenal's third, before Lee Carsley scored for Everton after Thomas Gravesen's sublime chip.
Substitute Robert Pires restored Arsenal's three-goal lead after Nigel Martyn spilled a low Henry shot.
It did not take long for Arsenal to resume the bewitching brand of football that saw them go undefeated in last season's Premiership.
With Bergkamp's wise head linking the play, Arsenal broke forward almost at will, utilising the speed of Reyes and Ljungberg on either flank and Henry in attack.
Three times in the opening 10 minutes Ljungberg, running from right to left, burst into the box.
On the third occasion he collected a Lauren pass, which required Nigel Martyn to rush out to smother the ball.
Moments later Lauren was again involved, this time in his own box, when he bravely blocked a Kevin Kilbane effort after Alessandro Pistone's long throw.
Play then switched to the Everton end and Gary Naysmith had to react quickly to hook Pascal Cygan's shot off the line.
Cygan looked rather less assured when he baulked a Kevin Campbell run, although referee Mike Riley waved play on.
The French central defender's partner Kolo Toure showed more authority when he rushed back to block a James McFadden shot.
Having allowed Everton that brief glimpse of goal, Reyes broke away in a counter-attack of bewildering speed to create the opening for Arsenal's opener.
Everton managed to halt Reyes' run into the box, but the ball only fell to Henry, who slipped a pass to Bergkamp, allowing the Dutchman to fire past the hapless Nigel Martyn.
Just before half-time Everton's defence switched off as they allowed Reyes to head past Martyn to convert a Ljungberg cross.
Soon after the interval more poor Everton defensive play allowed Arsenal to extend their lead.
Joseph Yobo's lazy pass went straight to Bergkamp, who threaded the ball out to Henry.
The Frenchman picked out Ljungberg in the box, who is unlikely to score a simpler goal this season.
Midway through the second half Everton finally managed to prise an opening in the Arsenal defence when a one-two between Gravesen and Carsley allowed the former Derby midfielder to pull a goal back.
Not that Arsenal were rattled and with seven minutes to go Pires tapped in from close range after Martyn was unable to hold a Henry shot.
Everton: Martyn, Pistone, Stubbs, Yobo, Naysmith, Osman,
Gravesen, Carsley, Kilbane, Campbell, McFadden.
Watson, Bent, Ferguson, Hibbert.
Arsenal: Lehmann, Lauren, Toure, Cygan, Cole, Ljungberg, Silva,
Fabregas Soler, Reyes, Bergkamp, Henry. Subs: Pires, Flamini,
Pennant, Almunia, Hoyte.
Referee: M Riley (W Yorkshire).