A controversial Laurent Koscielny goal deep into stoppage time against Burnley gave Arsenal a 1-0 win that puts them just two points behind City.
Pep Guardiola had previously won his opening six games to set the pace at the top of the league but had no answer for Mauricio Pochettino's Tottenham side in a 2-0 defeat earlier on Sunday.
Four points now separate the top five clubs while Spurs are the only side who remain unbeaten.
Wenger was celebrating 20 years at the helm of Arsenal and rumours are circulating this could be his last season.
If this is to be his final curtain at Arsenal, Wenger will be hoping to add some more silverware before he departs.
And with rivals Spurs beating City he expressed his relief that Arsenal were able to make the most of the opportunity to close the gap at the top of the Premier League.
“It’s a big win because City lost today,” Wenger said.
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“We were five points behind them and when you are five points behind a top quality team, when you have an opportunity to get a bit closer you cannot miss it.
"And that would’ve been the negative aspect of our game today had we not won.
“I must say, I am long enough in the job to know that you feel disappointed if you are in Burnley’s shoes because they gave absolutely everything and you can understand that they are a bit gutted to lose a game like that because they had put all the effort in to get the result.”