The club paid tribute to the Frenchman ahead of the match, and the players put on a fine performance for their manager to record their 15th home Premier League victory of the 2017-18 campaign.
The Gunners entered the match off the back of successive defeats to Manchester United and Atletico Madrid in the league and Europa League respectively, but never looked like losing to Burnley in the capital.
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.
The opening 12 minutes of the match passed without incident, but Arsenal made the breakthrough in the 14th minute following a smart move that originated down the right.
Indeed, Hector Bellerin found space in a forward position before cutting the ball back to Alexandre Lacazette, who played a one-two with Alex Iwobi before drilling a low cross towards Pierre-Emerick Aubameyang, who tapped home from close range.
Burnley hardly got out of their own half in the opening 30 minutes as Arsenal dominated the ball, although the Gunners were finding it difficult to build on their early advantage.
Arsenal were pressing though, and scored a second in the final stages of the first half when Lacazette turned a Bellerin cross into the back of the net to all but secure the points ahead of the second 45 minutes.
The Gunners came close to scoring a third early in the second half when Aubameyang poked a low cross in to Jack Wilshere, but the England international fired over the crossbar.
It was the home side that scored the game's third goal in the 54th minute, however, with Sead Kolasinac finding the far corner of the net with an excellent finish following smart work from Wilshere.
Iwobi was next on the scoresheet for Arsenal in the 64th minute, with the attacker smashing the ball into the top corner of the net from another Aubameyang assist.
Aubameyang then helped himself to his second of the match in the 75th minute with another smart finish from a Bellerin cross.
Danny Welbeck came within a whisker of making it 6-0 in the 88th minute with a ferocious shot, but the ball smashed against the post as Burnley desperately searched for the referee's final whistle, which arrived shortly after to put the Clarets out of their misery.
ARSENAL (4-3-2-1): Cech; Bellerin, Chambers (Mertesacker 77'), Mavropanos, Kolasinac; Xhaka, Wilshere (Ramsey 72'); Aubameyang, Iwobi, Mkhitaryan; Lacazette (Welbeck 72')
BURNLEY (4-4-1-1): Pope; Lowton, Long, Tarkowski, Ward; Lennon (N'Koudou 71'), Cork, Westwood, Gudmundsson (Wells 89'); Hendrick; Barnes (Vokes 22')