Norwich took the lead just before the hour through Michael Turner’s header from a Robert Snodgrass free-kick.
Mikel Arteta equalised from the spot after Kei Kamara was adjudged to have hauled over Olivier Giroud.
Giroud then touched in from Alex Oxlade-Chamberlain’s cross before substitute Lukas Podolski drove in a third in added time.
For 85 minutes, Arsene Wenger looked set to start a pivotal week for his team’s Champions League hopes with a defeat.
But, with games to come against Everton and Fulham before top-four rivals Tottenham are next in action against Manchester City on 21 April, his team answered plenty of questions about their quality and mental strength to secure a seventh win in eight Premier League matches.