Both teams formed a guard of honor for Wenger, 68, before kick-off to a chorus of "there's only one Arsene Wenger."
All around a full house of 60,000 at the Emirates — in stark contrast to recent league games when fans have stayed away in protest at a poor season — fans sported red t-shirts emblazoned with "Merci Arsene" (Thank you Arsene).
"I expect today will be dominated by sadness," wrote Wenger in his final program notes.
"It's the end of a long story for me at Arsenal. But I will also feel grateful for having led this club — that I cherish so much — for such a long time."
Wenger won three Premier Leagues and a record seven FA Cups. His crowning glory coming in the 2003/04 season when Arsenal won the league without losing a single game.
That "Invincibles" season was his last as a Premier League winner, though, and fans became tired of Arsenal's inability to compete for Premier League and Champions League titles.
However, there was plenty for the supporters to shout about in a fitting farewell for Wenger as Arsenal displayed the attractive brand of attacking football that characterized his most successful sides over the past two decades.
Defeat to Atletico Madrid in the Europa League semi-finals on Thursday means Arsenal missed out on Champions League qualification for the second consecutive season.
But they bounced back in style to secure the small consolation of ensuring they will finish sixth in the Premier League ahead of Burnley.
Wenger will wonder what might have been had Pierre-Emerick Aubameyang not been cup-tied for the latter stages of the Europa League as the Gabon striker took his tally to eight goals in 11 Premier League appearances since joining for a club record fee from Borussia Dortmund in January.
Aubameyang opened the scoring when he slid in to meet Alexandre Lacazette's cross to get a party atmosphere started after just 14 minutes.
Burnley have qualified for Europe for the first time in 51 years thanks to finishing seventh.
But it seemed incredible that only three points separated the sides before kick-off as Arsenal cut through the clarets at will going forward.
Lacazette stroked home Arsenal's second just before half-time before Jack Wilshere teed up Sead Kolasinac for a third nine minutes after the break.
Aubameyang turned provider for Alex Iwobi to smash home the fourth after being given a huge amount of time inside the Burnley box to pick his spot.
And Aubameyang finished as he started by steering home Hector Bellerin's cross to round off a five-star performance by the Gunners to send-off Wenger in style.
Wenger could even afford the luxury of also handing club captain Per Mertesacker an outing from the bench for the closing stages in his final home game before retiring at the end of the season.
And the margin of victory could even have been greater as Aubameyang unselfishly offered up the chance of a hat-trick by trying to square for Danny Welbeck, who just couldntarget="_blank"'>