Arsenal dominated the early stages, but were made to pay for not making the most of possession when Mohamed Diame put the Irons in front with a well-taken first goal for the club on 21 minutes. They dug deep and levelled through Olivier Giroud's first Premier League goal, with Theo Walcott and Santi Cazorla wrapping up the points.
Wenger's men will now head into the international break confident they can build a sustained attack on the top four. He said: "We started with a lot of questions raised about the team. We have now played seven games and the belief in the squad is that we have a chance."
He continued: "Of course we now need to do it week after week. The spirit and quality are there. It is about how consistent we are now."
Wenger added: "It was important for us to respond well and after our defeat against Chelsea, we won against Olympiacos on Wednesday night.
"We had a difficult game three days later and we knew a draw here was not good enough for us, so we went for it and gave absolutely everything to win the game."
Giroud, a ?12million signing from Montpellier, was recalled to the side on Saturday, and produced a determined display in a central striker role, converting Lukas Podolski's cross at the near post.
Wenger said: "He was good, had the physical presence and scored the goal. That will help him a lot to adapt very quickly."