Arsenal also ended the game with 10 men after France striker Olivier Giroud was sent off.
Giroud has struck 16 times in 21 games this season, a record that has attracted several clubs.
However, Giroud has revealed he is close to securing a deal with a top-level club - but not Celtic.
Olivier Giroud scored twice, while Lukas Podolski, Santi Cazorla and Theo Walcott were also on target for the Gunners.
It was Giroud who gave Arsenal the lead three minutes later touching in Alex Oxlade-Chamberlain's cross to send home fans delirious.
Arsenal paid more than double that to sign French striker Olivier Giroud, Spanish midfielder Santi Cazorla and German forward Lukas Podolski.
Cazorla's arrival at Arsenal follows the club's summer signings of Germany forward Lukas Podolski and France international striker Olivier Giroud.
Striker Van Persie was sold to Manchester United, with the likes of Lukas Podolski, Santi Cazorla and Olivier Giroud joining the Gunners.
After losing the first leg 3-1 at home on Feb. 19, Arsenal went ahead on Olivier Giroud's goal in the third minute.
Miss Giroud shared the shame of those French who believed the government should have fought on in 1940, but she had been sure that the Germans would be defeated.
Arsenal snatched a 3-2 win at second division Brighton as France striker Olivier Giroud scored twice and fellow forward Theo Walcott came off the bench to strike a decisive late goal.
Arsenal's French striker Olivier Giroud missed the best chance of the game, firing wide from eight yards out when stretching to meet a Aaron Ramsey cross, while Ross Barkley went close for the visitors.
Sergio Ramos gave the world and European champions an early lead which Cesc Fabregas failed to double when his first-half penalty was saved -- leaving the visitors to earn a deserved point when Olivier Giroud headed home deep in stoppage time.
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