Ozil created all of his side's goals at the Emirates Stadium and the result sent Arsenal top of the Barclays Premier League.
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 seal - 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.
"We have shown again another aspect as well, that we can dig deep and fight when we are a bit under pressure. When the third goal went in, we just kept the result."
The Arsenal manager was forced into a late change to his starting XI when England forward Theo Walcott suffered a minor abdominal strain during the warm-up and was replaced by German youngster Serge Gnabry.
"He had an abdominal muscle problem," said Wenger.
"Is it a question of days? I hope so. He had a little problem before the Marseille game and it became a bit worse.
"It is a bit mysterious because we don't really know what it is."
Denmark striker Nicklas Bendtner was on the bench for the first time this season, having seen a move away during the transfer window blocked, and could now feature at West Brom in the Capital One Cup next week.
Wenger said: "We have to rotate the squad because we play again on Saturday (at Swansea) and after that we have a massive home game in the Champions League."
Stoke manager Mark Hughes, meanwhile, felt his side could take great credit from their performance, despite the final result.
"We showed courage to get back into the match after the early goal," he said.
"We talked about trying to stay in the game in second half, and creating more opportunities for ourselves, and that is what we did with a level of control, but the third goal took the wind out of our sails."
The Stoke boss added: "Arsenal are a good team and have added a top-class player in Ozil, who had an influence today and I am sure that will continue."
Hughes was, though, less than impressed by the performance of referee Mike Dean and his assistants Gary Beswick and Jake Collin.
The Stoke manager said: "All people can have poor games and I think (Collin) had a poor game.
"I just felt his interpretation of some of the free-kicks and decisions which were given, both for and against (us)... I have seen that group of officials have better games, let's put it that way."