First Aaron Ramsey smashed in his seventh goal of an impressive season after Ozil's fifth-minute free-kick was parried by Stoke goalkeeper Asmir Begovic, but Geoff Cameron swept in a deserved equaliser for the visitors.
However, the class of Ozil - signed from Real Madrid on deadline day in a £43million deal - proved the difference as his corner was flicked home by compatriot Per Mertesacker to give Arsenal the lead once more before half-time, and then another pin-point deadball delivery made sure of all three points when Bacary Sagna looped in a header on 72 minutes.
"I believe that once he is completely integrated we will see even more of him, but he has shown today that he is a great player," said Wenger.
"Ozil is a player, when you look at his numbers, the assists are not a coincidence, it is just the reality of his game.
"You could see today he has a good pace as well. At the moment he focuses a lot on his passing, but he can create individually as well."
Arsenal have responded with seven straight wins since they were beaten 3-1 at home on the opening day of the season - and if Ozil continues his impressive displays, Wenger's squad could be set for a long-overdue sustained assault on the Premier League title.
Wenger, though, moved to play down any early talk of ending almost a decade without a trophy.
He said: "Ozil gave a lift to everybody at the club and, for the rest, it will be the quality of our teamwork and our team play that will decide that.
"The only thing of our position at the moment is that we are in a position where we can focus on improvement in a stable environment, so that is a good basis. For the rest, [in] the table everyone is mathematically together.
- Sports & Recreation
- Asmir Begovic
- Geoff Cameron
- Bacary Sagna
- Real Madrid