Michael Turner turned home Robert Snodgrass' free kick 11 minutes after the break to give the Canaries a shock lead at the Emirates, only for Mikel Arteta, Olivier Giroud and Lukas Podolski to net in the five minutes of the game to snatch a vital three points.
Arsenal play twice more before Tottenham's next Premier League fixture and could have opened up a seven-point gap before champions Manchester City travel to White Hart Lane on April 21 – and Wenger has expressed his delight at the Gunners’ form at the tail-end of the season.
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"Finishing in the top four is a question of nerve. Today was a balance of nerves, quality and intelligence. We didn't do anything stupid when we were 1-0 down. That side of the game is important.
"We need spirit and nerves. In the end we deserved the win. Credit to Norwich, they played well. They will not go down. They defended well, they gave us problems. We showed absolute resilience."
Another positive note to take away from Saturday’s win was the return of Jack Wilshere to the starting line-up, only for a fairly ineffectual performance seeing him replaced for Theo Walcott before the hour mark.
Wenger admitted that last week’s match-winner Tomas Rosicky’s absence through injury forced his hand in terms of the 21-year-old’s selection, before dismissing recent rumours of a summer exit for Podolski.
Wenger continued: "Wilshere worked hard. He’s in full training, and he and Walcott only got back into full training this week. We thought he had enough to play an hour. I wouldn't not have pushed him if Rosicky was available. I didn't want to restructure the team, so I put him in.
"Podolski is a luxury we have, as are Walcott and Alex Oxlade-Chamberlain. It’s very helpful. Look how we played when he came on. As soon as you have a player who doesn’t play for three games, there are stories in the paper."