The Dutchman's two goals took his tally to nine for Arsenal this season, while his previous double against Sunderland last Sunday once again helped his side secure three points.
But Wenger maintains his side are not reliant on Van Persie and praised his team's efforts against Tony Pulis' charges.
“When you want to be a team with quality, you always need one special player, someone like Thierry Henry. I don’t feel we are a one-player team. He [Van Persie] is an exceptional quality, of course,” he said.
“You can see that the team improved defensively, especially against a side that is challenging like Stoke.
“We looked much more solid defensively. We had a good start until they got the equaliser than I felt we became a bit nervous and lost our game.
“We needed half time to calm down and get back to our game. The second half was all us, especially after the first fifteen minutes and then the problem was to score goals.
“Robin can do that better than many people and he did it when he came on. Overall it was a good, spirited performance.
“Of course Robin, with the two goals, deserves massive credit but I feel Gervinho had a very lively and influential game."Gervinho opened the scoring for the hosts, before Peter Crouch leveled matters shortly before the break. Despite dominating possession, Arsenal struggled to break Stoke down and it looked as if the resilience of the visitors would be rewarded with a point before Van Persie’s cameo.
However, for the Gunners boss, the win was built upon the foundation of a markedly more assured defensive display from his side, with Laurent Koscielny and Per Mertesacker both enjoying sturdy performances.
“Credit to Stoke, they surprised us with the free kick and after that you could see that we were a bit in no man’s land. They took advantage of it,” said Wenger.
“From there frustration took over and our passing became less fluid until half time.
“We had a great response in the second half and the final part of the game was all us.
Wenger admitted Van Persie was close to being omitted from the matchday squad against Stoke due to the striker's recent run of fixtures coupled with his previous history with injuries.
“I was not even sure whether to involve him on the team sheet,” conceded Wenger.
“We had a check this morning and he was medically alright to be on the bench. I looked at the number of games he has played and the history he has. You need to be cautious.
“He played two full games for Holland, he played a whole game against Sunderland when he got back. He played up front alone in Marseille, so at some stage you have to give him a breather. He will be fit for Chelsea.”