The Germany international had a hand in all three of his side's goals on his home debut as Arsene Wenger's men eased to a comfortable win that sent them top of the Premier League ahead of Sunday's late fixtures.
Ozil's free-kick was parried into the path of Aaron Ramsey to score a fifth-minute opener, before Geoff Cameron cancelled that out for Stoke.
Per Mertesacker put Arsenal back in front at the break, with Ozil supplying the assist, before the £42.5million playmaker was on hand again to supply the third for Bacary Sagna to head home his first goal since February 2012 with 18 minutes left.
The only change for the hosts came just prior to the match, with Serge Gnabry called up as a late replacement for Theo Walcott, who was laid low with illness.
Mikel Arteta and Nicklas Bendtner both made their first appearances of the season on the bench.
For the visitors, Marko Arnautovic made his first start for the club in place of Matthew Etherington.
Arsenal had won their last six in all competitions going into the clash and they were ahead within five minutes through Ramsey.
Ozil's free-kick was parried away by Asmir Begovic and Ramsey followed up to finish at the near post and claim his fourth goal in three games.
Stoke responded well, and they were level through Cameron after 26 minutes, with the American coolly slotting home from outside the area.
Arnautovic saw his volleyed effort come back off the post, with the defender latching onto the rebound to put his side level.
Parity lasted just 10 minutes, though, and as Arsenal pressed forward, they were rewarded once again with the lead when Mertesacker put them back in front nine minutes before the break with his first goal of the season.
Ozil was the architect again as he swung in a corner and Germany international Mertesacker headed towards the far post, with the ball creeping in despite the efforts of the scrambling Begovic.
Olivier Giroud forced an impressive save from Begovic seven minutes after the break, following good work from Gnabry, before the French striker curled an effort over from inside the area soon afterwards.
Marc Wilson then had a sight on goal for Stoke just after the hour mark, but Wojciech Szczesny was equal to it and the Pole was soon required again, gathering a dangerous delivery from Steven N'Zonzi as the visitors applied pressure.
However, Arsenal went two goals clear courtesy of another header after 72 minutes, with Sagna getting his name on the scoresheet as he met another Ozil delivery and looped his header over Begovic and into the far corner.
Ozil was withdrawn to a standing ovation after 79 minutes, with Arteta on in his place, as Arsenal closed out the game to move top of the table.
