The last three league meetings between the teams were settled in Arsenal's favour by winners beyond the 90th minute, but the hosts made sure there was no need for late drama in Wenger's swansong.
Arsenal's next manager is to be handed a £200m transfer budget this summer, according to reports in the British media. There's no place for Mesut Ozil, but Per Mertesacker could come on for his final home game.
"This stadium I have worked on every single part from your press conference to the technical areas, so it is part of myself", said Wenger, who was given a hero's reception on a final lap of honour at full-time. "I will always be an Arsenal fan". "Thank you for having me for such a long time but above all, I'm like you - I'm an Arsenal fan".
After dodging more questions about who the club's next manager might be, and what he may do next himself, Wenger said how odd it often felt as a soccer manager to be asked frequently how he was feeling.
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Arsenal is yet to name Wenger's successor as the club faces its first managerial appointment since 1996.
Wenger will be determined to bow out on a victory with the Clarets able to move level on points with Arsenal in the Premier League.
Manager Arsene Wenger has bid farewell to the Emirates Stadium by calling on Arsenal's supporters to continue to back the team.
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".
Wenger, meanwhile, will ponder the next step in a career which has spanned over two decades at the club he loves.
"I would like to finish by one simple word: I will miss you".