In an entertaining clash, Theo Robinson gave the visitors the lead midway through the second half before Elliott Ward levelled with his first goal for Norwich.
The home side looked to have been held to a second successive draw until Lansbury popped up in stoppage time to give Paul Lambert's side a vital three points and preserve their place in the Championship top two.
Norwich started off the brighter as Russell Martin linked up well with Andrew Crofts but after the Welshman found Simon Lappin in the box, he was unable to keep his volley down.
Steve Morison had a chance for the visitors but his volley from distance just flew over John Ruddy's crossbar.
Norwich continued to attack with Andrew Crofts, who found Lappin, but the Scotsman failed to direct his effort on target. Simeon Jackson then skipped past the defence before shooting low at David Forde, but the goalkeeper was equal to the striker's effort.
Millwall had to make a substitution after 15 minutes with top scorer Morison limping off. His replacement Robinson almost made an instant impact, but Ruddy did well to tip his volley over the crossbar.
The Lions had a great chance to open the scoring on the half-hour when James Henry's corner found Darren Purse at the back post but the experienced defender fired over.
Canaries dangerman Grant Holt latched onto a Lappin pass but Jack Smith applied enough pressure to ensure Holt's effort from the edge of the box sailed wide.
The second half started controversially as Jackson went down in the area looking for a penalty but instead of pointing to the spot, the referee booked Jackson for simulation.
Millwall responded and took the lead on 57 minutes as former Norwich loanee Henry broke quickly before delivering a ball towards Robinson, and the former Huddersfield striker was on hand to place the ball past Ruddy from six yards.
Norwich went in search for an equaliser and Holt had a chance but could not direct his volley on goal from a Lansbury cross and Millwall could have snatched a second but Henry's shot was blocked by Marc Tierney.
The home side finally found an equaliser on 77 minutes when Lansbury's 25-yard free-kick came back off the post and Ward was on hand at the far post to smash the ball home and set up an exciting final 13 minutes.
Norwich applied the pressure in search of a winner and with the last kick of the game, the ball fell into the path of Lansbury who prodded home to give the Canaries a vital three points.