The club-record signing struck the free-kick on his home debut that led to Aaron Ramsey's fifth-minute opener, before crossing for his side's second and third - scored by Per Mertesacker and Bacary Sagna - as Wenger's men made it four consecutive Premier League wins.
In doing so, he began repaying a chunk of the £42.5million fee that brought him to the club from Real Madrid on transfer deadline day, but Wenger has not been surprised by Ozil's impressive start to life at Arsenal.
And he believes the Germany international playmaker still has even more to give.
"When you look at his numbers, his assists are not a coincidence, they are a reality of his game," Wenger said.
"I believe once he is fully integrated we will see even more from him.
"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."
On the game, Wenger was pleased to see two sides to his team's performance, claiming his charges showed fight in the face of second-half Stoke pressure.
"We had two halves. In the first we were fluent and (we played) well going forward," he continued.
"In the second half we looked jaded physically and lost our technical quality, but we showed another aspect - that we can dig deep and fight when we are a bit under pressure.
"It's been a very good week for us because we won in Marseille (in the UEFA Champions League), we won in Sunderland and we won today, so overall it's been a very positive week.
"When you play Stoke, you don't expect to score three goals from set-pieces but it shows us how important the delivery is."
