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 on 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.
Wenger said: "It is a question of nerves.
"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."
Wenger, though, conceded the longer Norwich held their own, the most testing it became.
"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," the Arsenal manager said.
"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."
As well as being less than impressed by the award of the spot-kick, Norwich felt it was never a corner in the first place.
Wenger, however, believes the calls were correct.
"The real question is was it a penalty or not? If it was a penalty, then it does not matter which end it is," he said,
"If you go into that kind of speculation we will question every single decision of the referee.
"What you have to question is was it a penalty or not? Everybody says yes."
Norwich boss Chris Hughton sought out the match officials following the final whistle, and was left frustrated by their explanations of the key decisions.
"We have only had one penalty all season, but we have had some poor decisions given against us," said Hughton.
"Sometimes there is momentum in a game, when the crowd start cheering, and sometimes people go along with those emotions.
"I will accept there was contact, but if he has pulled his shirt, he wont be the first player who has done that and in the balance of the game the referee has decided not to give it.
"We were on a day when the decisions went against us, but at 1-1 we did show a bit of naivety and we should have been good enough to keep it at that."
Norwich, who went on an unbeaten 10-match run at the turn of the year, still probably need at least five points to secure their top-flight status once again, with the visit of bottom club Reading to Carrow Road next weekend, followed by games against Stoke and Aston Villa set to define their campaign.
"We can gain a lot from this performance," Hughton said.
"Sometimes when you feel a little aggrieved, that can generate something in the group.
"We are at home in our next game (against Reading), and we need to do better in that."