Daniel Farke's side recorded their fifth successive victory in incredible fashion as Jordan Rhodes and Teemu Pukki turned the game on its head in the final minutes.
Pukki had cancelled out Tom Elliott's first-half opener and then saw his penalty saved by Millwall goalkeeper Ben Amos before Moritz Leitner edged the Canaries in front.
But in an astonishing final 11 minutes, Ryan Leonard and Jed Wallace thought they had pinched the points for struggling Millwall, only for Rhodes to level in the 92nd minute and Pukki to pounce in the seventh minute of stoppage time.
"It is important after a game like this for everyone to enjoy the moment, to feel the joy," said Farke, whose side are two points clear at the top.
"I want them all to make the most of it because sometimes players can wonder why they are doing all this hard work and this is the reason."