MILWALL were denied a point after an extraordinary finish at Carrow Road that saw five goals scored from the 79th minute and two in added-time for the home side to seal a 4-3 win.
Jordan Rhodes and Teemu Pukki scored in the 92nd and 97th minutes after Jed Wallace had given Millwall a 3-2 lead with seven minutes left.
Tom Elliott put Millwall in front when he headed home in the 24th minute, the first time the Lions had led away from home this season.
Five minutes before the break Norwich thought they had equalised when Christoph Zimmermann volleyed home after Timm Klose's header hit the crossbar, but the raised offside flag halted home celebrations.
Those fans weren't disappointed for long, as Pukki levelled four minutes into the second half.
The striker then had the chance to make it 2-1 after Murray Wallace was penalised for handball in the box, but Ben Amos saved Pukki's spot-kick.
The sides then traded quick goals when Moritz Leitner fired home from outside the box, before Ryan Leonard reacted to a second ball to poke past Tim Krul.
Incredibly, two minutes later, Wallace received a return pass from substitute Steve Morison to lift the ball past Krul.
But Norwich came back, and Rhodes scored two minutes into injury-time before Pukki collected substitute Mario Vrancic's pass to prod past Amos.
Millwall could have a complaint about the penalty given against them. Wallace was perhaps unlucky to be punished as he went in to block a shot, but his arm was slightly raised.
And the clock had ticked beyond the sixth minute of allotted injury-time when Pukki got his side's winner, though the referee has discretion to add extra time in addition to what goes up on the fourth official's board.
But the Lions really should have seen the game out after going ahead in the 83rd minute. They had enough defensive players on the pitch – after Ryan Tunnicliffe and James Meredith had come on, respectively, for Shane Ferguson in the 88th minute and Lee Gregory in the 92nd.
Millwall do not have the same defensive reliability as they had in the second half of last season, and it's now 29 goals conceded, already just 16 fewer than in all of 2018-19.
It's a similar story again going into the third international break of the season, and Neil Harris and his coaching staff must figure out how to stem the tide of goals against them.
Millwall take advantage of lax Norwich defending to lead at the break
You could hardly say Norwich, or any Championship side, wouldn't have known about Jake Cooper's effectiveness in the opponent's penalty area this season. He already had five assists – the most of any centre-back in the Championship – and when he jogged forward for a free-kick on halfway you would have expected the hosts to try to crowd him. They didn't, allowing the defender a free header back across goal for Elliott to aggressively attack it and head in.
Cooper's centre-back partner Shaun Hutchinson was doing a superb job at the other end, cutting out an attempted pass from Emi Buendia towards Pukki, before later in the half crashing into a tackle on Onel Hernandez to prevent him getting in on goal. Norwich fans felt the ferocity of it could have warranted a penalty, but Hutchinson had got the ball.
Amos tipped Timm Klose's header over the bar in the 35th minute as Norwich showed they also possessed a set-piece threat. And they had the ball in the net in the 40th minute, but the linesman judged Klose had strayed offside.
Norwich were getting their chances. A minute before the break Buendia curled a shot wide of Amos' left-hand post, and in first-half injury-time the goalkeeper was relieved to see left-back Jamal Lewis' attempted cross just miss the far top corner.
Millwall devastated after incredible finish
Norwich were transformed early in the second half, with Hernandez far more of a threat on the left wing against Conor McLaughlin, starting in place of Mahlon Romeo. Hernandez was involved in the Canaries' equalising goal when he helped the ball on to Marco Stiepermann, and Pukki jabbed home past Amos at the near post.
The striker then had the chance for his second in the 58th minute after Wallace handled in the area, but his spot-kick was too close to Amos, who made his fourth penalty save this season in all competitions.
Hutchinson risked a second booking when he challenged Krul for a high ball and appeared to catch the goalkeeper, but referee Jeremy Simpson didn't let the home players sway his decision and the Lions defender was relieved.
The game then entered a chaotic period with both sides believing they could win it.
It appeared it would be Norwich when Leitner gave Amos little chance after Millwall hadn't fully cleared far enough from their box.
But almost immediately from the kick-off Gregory challenged Lewis and Leonard pounced for his second of the season.
Wallace finished smartly for his second goal of the season, but this time it was Norwich who responded, Rhodes finishing low past Amos from Buendia's pass.
Deep into injury-time Millwall got a corner but Norwich cleared it and there was one last attack, Hutchinson unlucky to see the ball come off his foot and then Pukki as the Lions saw their winless away run stretch to 11 games this season.
Image: Millwall FC