The Dutch man of the match had a part in three first-half goals scored by compatriot Robin van Persie, Robert Pires and captain Patrick Vieira and then rounded off a fine performance with a deserved solo goal for Arsenal's sixth.
Before that Pires added a fourth early in the second half and Brazil midfielder Edu, who plans to leave Arsenal when his contract ends this season, scored the fifth with a penalty 20 minutes from time after a handball by Lee Carsley.
Midfielder Mathieu Flamini struck the seventh goal, his first for the club, five minutes from time at the end of a fine move started by fellow substitute Thierry Henry, back after a month out with a groin injury.
It was Arsenal's biggest Premier League victory.
Bergkamp, who was 36 on Tuesday, has been in discussions with the club over another one-year contract but Wednesday's game may have been his last at Highbury. He has said he will retire if an agreement with Arsenal is not reached.
"He's super-special, he had a hand in the first three goals and created a few other chances," Arsenal manager Arsene Wenger said, adding that he had already made up his mind about the Dutchman's future but would not reveal his decision yet.
Arsenal, who had already secured second place 11 points behind champions Chelsea with one game left, are at Birmingham City in their last league match of the season on Sunday.
They are 22 points in front of fourth-placed Everton.
Everton manager David Moyes began his brief post-match news conference by saying: "I'm embarrassed by tonight's performance.
"No criticism of the players but tonight as a manager, I'm totally embarrassed by what happened," he added and immediately walked out.
Henry's return pleased Wenger only 10 days before the FA Cup final at Cardiff's Millennium Stadium against Manchester United, who are third in the league nine points adrift of Arsenal.
"Thierry worked very hard for two weeks. We'll see how he responds (to the match)," Wenger said.
In a Dutch combination, Van Persie ran on to a superb ball that Bergkamp threaded through the Everton defence in the eighth minute to shoot low past goalkeeper Richard Wright.
Three minutes later, Bergkamp found Jose Antonio Reyes out on the left and the Spaniard pulled the ball back into the centre where Pires shot low past Wright.
The keeper dived full stretch to parry the ball upwards and Pires, following up, sent a looping header into the far top corner from close to the penalty spot.
Bergkamp was also involved in the third goal, which came from another fine move not long after the half hour mark that was finished by Vieira, who ran on to the Dutchman's pass to chip Wright as he dived at the French midfielder's feet.
The match also marked England defender Sol Campbell's return from an ankle injury layoff dating back to February 1. He played the full 90 minutes and earned a booking for a tackle from behind on Everton substitute Duncan Ferguson.
"Sol got stronger and stronger through the game," said Wenger.