A virtuoso performance from Dennis Bergkamp inspired Arsenal to victory.
Thanks to Bergkamp's vision and touch Arsenal had scored twice in the opening 12 minutes, the Dutchman setting up Robin van Persie and Robert Pires.
Bergkamp's pass for Arsenal's third was even better, releasing Patrick Vieira who deftly chipped Richard Wright.
After the break Pires bagged a second, Edu fired in a penalty, Bergkamp capped a superb display with the sixth, with Mathieu Flamini completing the rout.
Arsenal's control was so total that manager Arsene Wenger was able to introduce Thierry Henry after the break, the Frenchman's return from a groin injury a timely boost ahead of the FA Cup Final.
Everton were restricted to a few hurried shots, two from Mikel Arteta and one from James Beattie.
The margin of Arsenal's victory - a record win under Arsene Wenger and a record defeat in the Premiership for Everton - was even more astonishing given the Toffees' qualification for the Champions League.
Visiting manager David Moyes, who had asked his team to enjoy the occasion after securing fourth place in the Premiership, ordered them to go and apologise to their travelling fans at the end.
HEAVIEST PREMIERSHIP DEFEATS
Man Utd 9-0 Ipswich, Mar 95
N'castle 8-0 Sheff W, Sep 99
Nottm For 1-8 Man U, Feb 99
Arsenal 7-0 Everton, May 05
B'burn 7-0 Nottm For, Nov 95
Man U 7-0 Barnsley, Oct 97
Arteta's first effort came before Arsenal scored their opener, a miss that was to prove costly.
Bergkamp has still not yet been offered a new contract by Arsenal, but on the evidence of his performance he is likely to be finding gainful employment at Highbury come the start of the new season.
The Dutchman, who turned 36 on Tuesday, was by far the best player on the pitch, his every touch, his every pass, drawing appreciation from the Highbury crowd.
First Bergkamp slipped a pass through to Van Persie that completely cut out the Everton defence.
Without breaking stride, Van Persie curled the ball past Wright.
After displaying the art of the short pass, Bergkamp showcased his long passing skills, freeing Van Persie, who was lurking on the left.
The former Feyenoord winger pulled the ball back for Pires, whose initial shot was well saved by Wright.
However luck was against the Everton keeper as the ball went straight to Pires, who cleverly flighted a lobbed header over Wright.
As Arsenal warmed to the task of entertaining Highbury for its final game of the season, Edu's dummy created a space for Vieira, whose swerving shot went narrowly wide.
Vieira was soon on the scoresheet as he delicately chipped Wright after the Frenchman was released by another exquisite Bergkamp pass.
After the interval Bergkamp was quickly back to work, twice releasing Henry, who first fell under a clumsy tackle from Joseph Yobo and then was just unable to reach the Dutchman's cross.
The fourth goal arrived on 50 minutes, with Bergkamp once again involved.
He clipped the ball into Henry, whose pass found its way to Pires after a deflection off Carsley.
Pires effortlessly stroked the ball past Wright to claim his second of the game.
Carsley handled a Henry pass to give away the penalty.
The Arsenal team asked Edu to take the spotkick, the Brazilian scoring in his final Highbury appearance despite Wright getting a hand to the shot.
Bergkamp brought the house down when he scored Arsenal's sixth, clipping the ball past Wright.
Arsenal refused to rest on their laurels and Flamini added a seventh with a half-volley after good work from Henry and Jose Antonio Reyes.
Arsenal: Lehmann, Lauren, Campbell, Senderos, Cole, Pires (Fabregas 64), Vieira (Flamini 45), Edu, Reyes, Bergkamp, Van Persie (Henry 45). Subs Not Used: Almunia, Toure.
Booked: Flamini, Campbell.
Goals: Van Persie 8, Pires 12, Vieira 37, Pires 50, Edu 70 pen, Bergkamp 77, Flamini 85.
Everton: Wright, Hibbert, Weir, Yobo, Pistone, Carsley, McFadden, Watson, Arteta (Ferguson 75), Kilbane, Beattie (Bent 45). Subs Not Used: Stubbs, Plessis, Turner.
Ref: A Wiley (Staffordshire).