With Chelsea's FA Cup semi-final date at Wembley meaning their clash with Tottenham was postponed, the Gunners had the perfect opportunity to put themselves back in the driving seat for Champions League qualification.
However, heading into the final five minutes at the Emirates Stadium on Saturday, that looked an unlikely prospect as the Canaries were still resolutely defending their lead from Michael Turner's close-range header just before the hour.
The match turned, though, when assistant referee Richard West on the far side signalled a shirt pull by Kei Kamara against Olivier Giroud - much to the disbelief of the Norwich players, who surrounded Mike Jones after he had initially not given the penalty decision.
Mikel Arteta kept his cool from the spot to slot low past the dive of Mark Bunn, booked for his protests, before Giroud tapped in to complete the comeback after 88 minutes and substitute Lukas Podolski crashed home a third in stoppage time, with more than a hint of offside in the build-up, to ensure a flattering scoreline for the home side.
Nevertheless, it was a hard-fought victory by Wenger's men, whose run of eight wins in 10 Premier League games has clawed them back into the driving seat for top-four finish.
Indeed, Arsenal will play twice more - at home to Everton on Tuesday night and then at Fulham - before Spurs kick off against Manchester City at White Hart Lane on Sunday.
"It is a question of nerves," said Wenger. "The win over Norwich was a balance of nerves, quality and intelligence. We did not do anything stupid when we were 1-0 down and kept faith in our game. That side of the game will be important.
"We know we cannot drop points and we have to go until the end with this consistency. In these type of games, you need to open it up and to do that you have to score, but we did not do that.
"Then you think 'let's not make a mistake', and you lose a bit of your spontaneous fluency and it becomes a bit more difficult."