Steve Morison's late equaliser earned Norwich a draw that left a major dent in Arsenal's Champions League hopes.
Yossi Benayoun curled in a shot with barely a minute gone but Wojciech Szczesny somehow allowed Wes Hoolahan's tame effort to beat him.
Grant Holt's deflected shot put Norwich ahead but Robin van Persie levelled with a volley and completed the comeback with a well-hit second.
But Morison's cross-shot pulled the Canaries level in a thrilling finish.
The result extends Arsenal's winless run to four games, and seriously damages their chances of qualifying for the Champions League.
Arsene Wenger's fate is no longer in his own hands - the Gunners, who are two points clear in third place, can be overhauled on Sunday when north London rivals Tottenham travel to Aston Villa and Newcastle host Manchester City.
After last week's 1-1 draw at Stoke, Wenger admitted that his team were over-reliant on Van Persie's goals, and this performance did little to disprove that view.
Van Persie, who only has one year remaining on his contract, thought he had once again come to his side's rescue when he extended his remarkable goal tally to 37, but Norwich substitute Morison had other ideas.
Wenger could point to referee Anthony Taylor's failure to award a penalty for Kyle Naughton's blatant push on Van Persie in stoppage time but Norwich's positive approach and impressive late defending certainly merited a point.
The Arsenal manager had insisted that there should be no need for nerves from his players, but even if there was any anxiety it should have been disappeared when Benayoun swept in.
Tomas Rosicky seized on a loose clearance to pick out the Israeli, who used an overlapping run from Kieran Gibbs to dummy and create the space to bend a shot into the far corner.
Despite their recent slump, Norwich responded well and they pulled level when Naughton pulled back and Szczesny made a mess of Hoolahan's first-time shot.
The visitors pulled ahead just before the half-hour, when Hoolahan threaded through for Holt to hit a shot that looped up off Gibbs and over Szczesny.
After losing Bacary Sagna to what appeared to be an ankle problem, things could have got even worse for the hosts.
Benayoun got away with kicking out at Ryan Bennett and Norwich had valid penalty appeals for Francis Coquelin's sliding tackle on Hoolahan and Laurent Koscielny's tug on Martin.
Simeon Jackson should have added a third after the break when he tore away from Thomas Vermaelen only to fail to trouble Szczesny.
Rosicky's free-kick picked out Benayoun but the on-loan Chelsea midfielder headed straight at John Ruddy.
It was by no means one-way traffic, though, and Hoolahan clipped a volley wide from a neat Holt flick at the other end.
Van Persie had barely been involved but the Dutchman made no mistake after 71 minutes when he volleyed in from Alex Song's fine pass.
The Dutch international had a stabbed effort held by Ruddy but put Arsenal in front when his shot from just inside the area had enough power to beat Ruddy.
But Morison pulled the visitors level once again when he raced on to a through ball and drove a shot across Szczesny for his first goal since January.
Still the chances came thick and fast. Ruddy saved from Van Persie, who was then denied a late penalty when he went down under a barge from Naughton before the Norwich goalkeeper pulled off a fine block from Song.
And Ruddy was outstanding once again as he somehow got a hand to a header from Gibbs, giving Norwich a well-deserved point which could have far-reaching consequences.
Arsenal manager Arsene Wenger:
"Here the whole season we have got zero penalties. It is absolutely amazing, because you see other clubs who have got 10.
"I don't know (why the penalty was not given), we have to accept the decision of the referee.
"It is more than frustrating because we were very poor in the first half, not switched on."
Norwich manager Paul Lambert:
"I've said to the players that I'm so proud of what they've given this season and this highlighted it even more. We were outstanding.
"I thought Spurs was as good as anything in my time here but this might surpass it.
"We wanted to get on the front foot and everyone was outstanding. We could have been 3-1 up when Simeon went through and should have had a penalty in the first half. They might think they should have had a penalty at the end but Gervinho was offside."