Goals from Theo Walcott and Olivier Giroud before halftime allowed Arsenal to move to within two points of surprise leaders Leicester City and four clear of City ahead of the busy holiday fixture list.
With champions Chelsea seemingly out of the picture after a calamitous start, Manchester United wobbling and Liverpool also off the pace, talk of a first Premier League title since 2003-04 is rife in north London.
Wenger, however, is not getting ahead of himself.
"It's too early to say we can win the league, but it strengthens our belief," he told reporters.
"You realise you earn your right to win these games and for us it is important that we realise that we have to be ready to fight like that in every single game.
"But it is a significant game because when you look at Manchester City and the quality they have on the pitch, we know at the end they will be there fighting for the championship."
He revealed that Mesut Ozil, who set up both Arsenal's goals, had barely trained all week because of illness.
"He had a chest infection for the week and was in bed basically," Wenger added. "So for a guy that could not prepare or work well he has done well physically."
He also praised the German playmaker's growing influence as he returns to the kind of form he displayed when he first signed for the Gunners from Real Madrid in 2013.
He has been provided more assists (15) than any other player in England so far this season.
"He is much more mature, much more keen to take responsibility, I personally believe he has developed his physical attributes, his physical commitment. You see his desire to win," Wenger said.
(Reporting by Marc Jones; editing by Martyn Herman)
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