The Gunners came from behind to record a 3-1 win over their visitors, with Theo Walcott, Mesut Ozil and Alex Iwobi striking after Charlie Adam marked his 31st birthday with a penalty to put Stoke ahead.
The result means Arsenal are unbeaten in the league since their opening weekend loss at home to Liverpool and it took them top of the table on goal difference from Chelsea, who face West Brom on Sunday.
But overnight at least, Wenger could toast being at the top as he looks for a first league title since 2004, and the Frenchman insists his side will be there or thereabouts come the end of the campaign.
“It’s good. But let’s wait until tomorrow,” he said when asked about going top.
“At the minute there is no difference anyway with the other teams, there is Chelsea v West Brom tomorrow. But we are in there. No matter what the results will be. So that’s good – we are in the fight.
“We were not too bad last year. We finish second in the league. I believe we have improved, yes. But we have to show that on a longer term.
“I believe that we have created confidence, I think we are ambitious – but what is at stake is to keep urgency levels very high, humility levels very high and togetherness very high. We have to show that in every single game now. Then we will see where we stand.”
Despite moving to the top, Wenger still wants to see further improvements on last season, when Arsenal finished a distant second to surprise champions Leicester, starting with this kind of performance against mid-table opposition.
Wenger said: “When you analyse last season at home, we did very well against the top five and we dropped points between fifth and 12th at home, teams in mid-table.
“Certainly that is our challenge this year, to continue to do well against the top teams but as well in these kind of games, like Stoke today, where you have to win and we dropped some points last year.”
Wenger was not happy at the award of Stoke’s penalty as referee Lee Mason pointed to the spot following a collision between Joe Allen and Granit Xhaka.
Xhaka caught the Stoke midfielder with his elbow, however, and after Adam stroked home the resulting penalty, Arsenal were rattled. They had already lost Shkodran Mustafi to a hamstring injury.
But they levelled just before the break as Walcott swept home a low cross from Mustafi’s replacement, Hector Bellerin, and were ahead after the interval when Ozil headed in Alex Oxlade-Chamberlain’s ball.
The points, and a place at the head of the Premier League, were assured when substitute Iwobi finished well after Mason had played an advantage following a foul on Alexis Sanchez.