Ryan Giggs marked his 900th appearance for Manchester United with a dramatic late winner as Sir Alex Ferguson's side closed the gap on leaders Manchester City to two points.
United took an early lead when Paul Scholes headed home Nani's cross.
Grant Holt levelled for the Canaries late on when he held off Rio Ferdinand to turn and fire into the top corner.
But there was still time for Giggs to steal the points when he converted Ashley Young's cross at the far post.
Giggs, who made his league debut 21 years ago next month, was impressive throughout and had already hit the crossbar with a cushioned volley in the second half before his stunning late intervention.
But the result was harsh on a Norwich side who caused United no end of problems and were only denied further goals by the excellence of goalkeeper David de Gea.
The Spaniard pulled off fine saves to deny Holt, Anthony Pilkington and Aaron Wilbraham before he was finally beaten by Holt with just seven minutes left.
That goal kicked United into gear and, when Young whipped in a dangerous cross from the left, Giggs arrived unmarked to clip the ball through John Ruddy's legs.
Ferguson's side had seen City move five points clear with their 3-0 defeat of Blackburn on Saturday and started in the manner of a side eager to close the gap.
Ryan Giggs in the Premier League
- 584 appearances
- 107 goals
- 375 wins
- 79 defeats
- 12 title medals
Giggs came close to a spectacular opener inside five minutes when he arrived on Phil Jones' cross but volleyed high and wide at the back post.
Jones was not even born when Giggs first featured for United, but the young defender played his part moments later as another veteran put the champions ahead.
Scholes spread the ball out to Jones on the right, who laid the ball back to Nani. The winger took a touch before delivering a teasing cross which evaded Javier Hernandez and Danny Welbeck but not Scholes, who timed his run to perfection to arrive unmarked to head into an open goal.
Scholes was at the heart of everything from United in the opening half, and his surprise decision to come out of retirement last month is already looking like a masterstroke for the champions.
Welbeck was denied by a fine save from Ruddy, but it was the hosts who bossed the rest of the half and only some brilliant goalkeeping kept United head.
First De Gea saved with his feet to keep out Pilkington's shot, before he held on to Holt's close-range header.
Norwich were unable to apply the same pressure after the break, and Welbeck came close to a second when he collected a perfect Giggs through-ball but saw his chip cleared off the line by Zak Whitbread.
The sole slack pass of the afternoon from Scholes led to Wilbraham testing De Gea with a rising 20-yard strike, before Norwich did find a way through.
A corner was half cleared, Adam Drury pumped the ball back in to the area and, when Whitbread headed on, Holt showed great touch and strength to turn Ferdinand and thrash his left-footed shot into the top corner.
The joy was shortlived for Norwich fans, however, as Giggs signed off the latest chapter in his incredible career with his 107th Premier League goal to keep him in the hunt for a 13th league medal.
Norwich manager Paul Lambert:
"We were excellent but that's what happens against United.
"They've done that for years and years. We were running on empty at the end but we put in a massive effort.
"There is nothing to be ashamed of, we gave a really good account of ourselves."
Manchester United boss Sir Alex Ferguson:
"Norwich deserved a point today and it was a great goal they scored, but at that moment you saw us as Manchester United.
"I am sure this result will have an impact on the season.
"Everyone knows we never give in, no matter who plays us, they know they will have to play right to the death."
Live Text Commentary
Full Time The match has reached full-time.90:00 +2:39 Substitution
Substitution Ryan Giggs leaves the field to be replaced by Chris Smalling.90:00 +2:10 Booking
Booking Booking for Rio Ferdinand for dissent.90:00 +1:10
Assist on the goal came from Ashley Young.90:00 +1:10 Goal scored
Goal! - Ryan Giggs - Norwich 1 - 2 Man Utd Ryan Giggs grabs a goal from close in to the bottom right corner of the goal. Norwich 1-2 Man Utd.90:00 +1:05
The ball is delivered by Ashley Young,90:00 +0:25
Corner taken by Luis Nani played to the near post, Andrew Surman makes a clearance.90:00 +0:19
Luis Nani crosses the ball, Elliott Ward makes a clearance.89:35
Phil Jones sends in a cross, John Ruddy makes a save.89:13
The ball is delivered by Luis Nani, Zak Whitbread makes a clearance.88:59
Danny Welbeck takes a shot. Save by John Ruddy.88:51
Centre by Phil Jones, Elliott Ward manages to make a clearance.87:38
Ashley Young gives away a free kick for an unfair challenge on Kyle Naughton. Free kick taken by John Ruddy.86:07
Ryan Giggs produces a cross.85:25
Centre by Michael Carrick, Ashley Young takes a shot. Blocked by Kyle Naughton.84:58
Adam Drury sends in a cross, Grant Holt takes a shot. David De Gea makes a save.84:07
The ball is swung over by Luis Nani, John Ruddy makes a save.82:56
The assist for the goal came from Zak Whitbread.82:56 Goal scored
Goal! - Grant Holt - Norwich 1 - 1 Man Utd Grant Holt finds the back of the net with a goal from inside the box to the top left corner of the goal. Norwich 1-1 Man Utd.82:36
Corner taken left-footed by Andrew Surman from the right by-line, save made by David De Gea.
Aaron Wilbraham takes a shot. Save made by David De Gea.81:43
Elliott Bennett produces a cross.80:58
Free kick awarded for a foul by Kyle Naughton on Ashley Young. Direct free kick taken by Ashley Young.79:14
Kyle Naughton sends in a cross.78:45
Danny Welbeck takes a shot. Save made by John Ruddy.76:50
The ball is sent over by Luis Nani, clearance by Adam Drury.76:08
Centre by Wesley Hoolahan, clearance by Ashley Young.75:05
Danny Welbeck fouled by Elliott Ward, the ref awards a free kick. Ashley Young takes the free kick.73:39
The ball is sent over by Wesley Hoolahan, Headed effort from deep inside the penalty area by Grant Holt goes harmlessly over the crossbar.73:31
David Fox delivers the ball, clearance made by Paul Scholes.73:07
Free kick awarded for a foul by Patrice Evra on Wesley Hoolahan. Free kick taken by Kyle Naughton.71:52
Phil Jones delivers the ball, Effort on goal by Ryan Giggs from 12 yards.70:33
Kyle Naughton sends in a cross.69:37 Substitution
Substitution Aaron Wilbraham replaces Anthony Pilkington.68:55
Wesley Hoolahan takes a shot from just outside the penalty area which clears the crossbar.67:48
A cross is delivered by Ryan Giggs, Elliott Ward manages to make a clearance.67:25
Elliott Bennett produces a cross, save made by David De Gea.66:06
Corner taken by David Fox played to the near post, clearance made by Ryan Giggs.66:00
Anthony Pilkington produces a cross, Phil Jones manages to make a clearance.65:40
Kyle Naughton delivers the ball, clearance by Phil Jones.64:25
Corner taken left-footed by Ryan Giggs to the near post, save by John Ruddy.63:46
Shot from 6 yards by Danny Welbeck. Zak Whitbread makes a clearance.62:22 Substitution
Substitution Javier Hernandez goes off and Ashley Young comes on.62:22 Substitution
Substitution Elliott Bennett on for Bradley Johnson.62:13
Anthony Pilkington sends in a cross.62:02
Luis Nani crosses the ball.61:06
The ball is crossed by Phil Jones, clearance by Zak Whitbread.59:10
Centre by Anthony Pilkington, Andrew Surman takes a shot. Michael Carrick gets a block in.58:21
Javier Hernandez gives away a free kick for an unfair challenge on Zak Whitbread. Free kick taken by Zak Whitbread.57:45
Bradley Johnson has an effort at goal from outside the penalty box which goes wide left of the goal.56:49
Danny Welbeck is penalised for a handball. John Ruddy restarts play with the free kick.56:40
The ball is sent over by Danny Welbeck, Zak Whitbread manages to make a clearance.56:10
The referee blows for offside. Free kick taken by Elliott Ward.55:47
Anthony Pilkington crosses the ball, clearance made by Jonathan Evans.46:31
Andrew Surman has a headed effort at goal from close in which goes wide left of the goal.47:55
Foul by Jonathan Evans on Wesley Hoolahan, free kick awarded. Direct free kick taken by Elliott Ward.47:55 Booking
Booking The referee shows Jonathan Evans a yellow card for unsporting behaviour.47:07
Corner taken by Ryan Giggs from the right by-line to the near post, clearance made by Kyle Naughton.45:01
The referee starts the second half.45:00 +2:34
Header from close in by Andrew Surman misses to the right of the goal.45:00 +2:23
The ball is crossed by Anthony Pilkington, clearance by Rio Ferdinand.45:00 +2:11 Half time
Half Time The ref blows to signal half-time.45:00 +2:08 Substitution
Substitution Wesley Hoolahan joins the action as a substitute, replacing Simeon Jackson.45:00 +2:01
The ball is swung over by Adam Drury, David De Gea makes a save.45:00 +1:22
The ball is sent over by Luis Nani, save made by John Ruddy.45:00 +0:33
Unfair challenge on Jonathan Evans by Grant Holt results in a free kick. Free kick taken by Jonathan Evans.40:23
Free kick awarded for a foul by Grant Holt on Luis Nani. Phil Jones takes the free kick.37:50
The ball is sent over by Kyle Naughton, Rio Ferdinand manages to make a clearance.37:15
Simeon Jackson takes a shot. Blocked by Jonathan Evans.36:21
Andrew Surman has an effort at goal. Phil Jones gets a block in.35:54
Foul by Phil Jones on Grant Holt, free kick awarded. Free kick taken by Adam Drury.33:45
Centre by Anthony Pilkington, Grant Holt takes a shot. Save by David De Gea.32:25
Javier Hernandez takes a shot. John Ruddy makes a save.31:13
Unfair challenge on Simeon Jackson by Jonathan Evans results in a free kick. David Fox delivers the ball from the free kick right-footed from left channel, save by David De Gea.29:56
Patrice Evra crosses the ball, clearance made by Elliott Ward.28:42
Jonathan Evans challenges Simeon Jackson unfairly and gives away a free kick. The free kick is swung in right-footed by David Fox, Phil Jones manages to make a clearance.28:02
Kyle Naughton has a shot on goal from outside the box which misses right.27:48
Anthony Pilkington takes a shot. David De Gea makes a save.27:28
Bradley Johnson produces a cross, Paul Scholes manages to make a clearance.27:13
The ball is delivered by Simeon Jackson, clearance by Rio Ferdinand.25:12
Bradley Johnson sends in a cross, Headed effort on goal by Grant Holt from inside the penalty box misses to the right of the goal.23:20
Andrew Surman produces a left-footed shot from 35 yards and went wide right of the net.22:28
Unfair challenge on Simeon Jackson by Patrice Evra results in a free kick. David Fox crosses the ball in from the free kick, clearance by Rio Ferdinand.21:09
The ball is swung over by Anthony Pilkington, Rio Ferdinand makes a clearance.20:35
Inswinging corner taken by Andrew Surman from the right by-line played to the near post, Luis Nani manages to make a clearance.19:41
Andrew Surman fouled by Phil Jones, the ref awards a free kick. David Fox delivers the ball from the free kick right-footed from left wing, clearance made by Rio Ferdinand.18:53
The ball is delivered by Anthony Pilkington, clearance made by Phil Jones.17:10
Free kick awarded for an unfair challenge on Patrice Evra by Bradley Johnson. Patrice Evra takes the direct free kick.15:52
Inswinging corner taken right-footed by Luis Nani, Paul Scholes takes a shot. Blocked by Elliott Ward.15:33
Centre by Javier Hernandez, Danny Welbeck takes a shot. Save by John Ruddy.14:30
Javier Hernandez is caught offside. Free kick taken by Elliott Ward.13:48
The ball is crossed by Luis Nani, Zak Whitbread manages to make a clearance.13:06
Free kick awarded for a foul by Grant Holt on Paul Scholes. Paul Scholes takes the free kick.12:05
Free kick awarded for an unfair challenge on Danny Welbeck by Bradley Johnson. Direct free kick taken by Rio Ferdinand.11:57
The ball is swung over by Simeon Jackson, Rio Ferdinand makes a clearance.11:12
Foul by Luis Nani on David Fox, free kick awarded. Direct free kick taken by John Ruddy.9:28
Michael Carrick takes the free kick.9:28 Booking
Booking Booking for Bradley Johnson for unsporting behaviour.9:21
Luis Nani fouled by Bradley Johnson, the ref awards a free kick.7:36
Simeon Jackson challenges Jonathan Evans unfairly and gives away a free kick. David De Gea takes the free kick.6:31
Assist on the goal came from Luis Nani.6:31 Goal scored
Goal! - Paul Scholes - Norwich 0 - 1 Man Utd Paul Scholes grabs a headed goal from close range. Norwich 0-1 Man Utd.6:30
The ball is sent over by Luis Nani,6:06
Centre by Phil Jones, clearance by Adam Drury.5:11
Phil Jones crosses the ball, Ryan Giggs has an effort at goal from deep inside the area missing to the left of the goal.5:00
Luis Nani sends in a cross, clearance made by Adam Drury.4:24
The ball is sent over by Phil Jones, Zak Whitbread makes a clearance.0:46
Anthony Pilkington produces a cross, save by David De Gea.0:16
A cross is delivered by Simeon Jackson, David De Gea makes a save.0:00
The referee gets the match started.
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