Ozil put Arsenal ahead in the 13th minute before Alexandre Lacazette's quickfire double and late strikes from Rob Holding and Eddie Nketiah against a youthful PSG side.
The International Champions Cup win in Singapore was also a boost for Arsenal's new manager Unai Emery against his former club, now under Germany's Thomas Tuchel.
Ozil, named as captain after his torrid week, was quickly into his stride with midfield partner Henrikh Mkhitaryan against a PSG line-up shorn of its World Cup stars.
He opened the scoring with a tap-in at the far post after Mkhitaryan released Pierre-Emerick Aubameyang in space and the Gabonese forward passed back across the face.
Ozil's exquisite flick during a length-of-the pitch move nearly produced Arsenal's second but Gianluigi Buffon saved well from Nigeria's Alex Iwobi.
The Italian great also denied Aubameyang and Mkhitaryan, while at the other end teenager Timothy Weah twice went close and Christopher Nkunku curled one over.
After the break, an Nkunku free kick drew a flying save from Arsenal substitute Emiliano Martinez, before Weah went down for a 59th-minute penalty which Nkunku converted with aplomb.
But Lacazette hit back with two goals in four minutes -- first a sumptuous, near-post heel-flick which sailed past the nonplussed Buffon, and then a close-range header.
Substitute defender Holding added the fourth with a towering header on 87 minutes, before Nketiah swept home Arsenal's fifth with the last kick of the game.
Ozil, who is of Turkish heritage, sent shockwaves through Germany this week when he quit the national team complaining of "racism and disrespect" from football authorities.