Arsenal, who will finish sixth in the Premier League table this season, now face a trip to Leicester City on Wednesday night before ending their season at Huddersfield Town next weekend, while seventh-placed Burnley finish at home to Bournemouth.
Burnley hardly got out of their own half in the opening 30 minutes as Arsenal dominated the ball, although the Gunners were finding it hard to build on their early advantage.
This was Wenger's 606th and final home game in charge of Arsenal (W415 D120 L71), with this the 27th time that his team have won by five or more goals on home soil.
"What I will miss most about this job is the competition itself", Wenger said in his final programme notes.
"That means involving at least three players every move, to express your talent, and make people feel that when football is expressed in a collective way and with a high understanding, it's art".
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"And reacting to Wenger's final game in charge at The Emirates, Morgan wrote on Twitter: "[Wenger] left us 6th in the Premier League, having to qualify for the Europa League, and with a squad full of very average, overpaid wastrels.
Chants of "There's only one Arsene Wenger" and "Arsene give us a wave" could be heard from the stands at regular intervals, while the majority of the 59,549 in attendance donned red T-shirts handed out by the club with the message "Merci Arsene".
"I can say guys who managed 22 years in a club of that stature, there are not many".
"For me this group of players has a special quality, not only on the pitch but also off it".
"I would like to wish my fellow manager Alex Ferguson well and hope he gets well quickly". And please, support this team and push next season, because they deserve it. For 20 years, I just felt, "OK, forget about me, and just care about the problems you have to sort out". Thank you for being such an important part of my life.