Grant Holt's injury-time strike earned Norwich a first Premier League win in 10 games as they scored twice in the final six minutes to stun Everton.
Canaries substitute Kei Kamara's towering late header seemed to have rescued a point for the Canaries.
But Holt grabbed an unlikely winner when he stabbed the ball in from close range four minutes into added time.
A first for Sierra Leone
Kei Kamara is the first player from Sierra Leone to score in England's top flight and his goal means that players from 88 different nations have now scored in the Premier League.
Everton had deservedly led through Leon Osman's close-range header before their capitulation in a remarkable finale.
The result is a huge blow to the Toffees and their hopes of securing a Champions League qualification place.
But they seemed certain to keep the pressure on the top four and stay within two points of
as they dominated the early stages of the second period, retaining possession with ease and frustrating their hosts.
There was certainly no sign of the late drama to come as Everton eased into a half-time lead.
Hughton salute 'big win' for Norwich
Osman grabbed the goal when he headed home a teasing Leighton Baines cross six minutes before the break after a fine move on the left flank which also involved Steven Pienaar and Marouane Fellaini.
Nikica Jelavic had earlier been denied by Mark Bunn when the goalkeeper blocked well with his feet after a smart turn and piece of control in the six-yard box, and Bunn also kept out a deflected cross from fit-again right-back Seamus Coleman.
And, although the visitors did not create many clear-cut chances, they always posed the greater threat.
A Holt shot that was well saved by Tim Howard when the scores were level was as good as it got for Norwich before the interval.
Kamara headed narrowly wide from an inviting right-wing centre and that rare chance seemed to lift the home crowd and bring much-needed belief.
Nigel AdderleyMatch of the Day commentator
That could be a moment to transform Norwich City's season. It has been such a grim mid-winter all around Carrow Road and Chris Hughton must be ever so relieved. It was captain Grant Holt who grabbed the winner but it was Kei Kamara who inspired the fightback.
With the pressure mounting, Kamara headed Norwich level with his first Premier League goal when he powered home a Robert Snodgrass corner.
And, much to Everton manager David Moyes' disgust, Holt reacted quickest to bundle home the winner from close range after the scheduled three minutes of added time has passed.
Norwich manager Chris Hughton:
"Once you are 1-0 down and you get back to 1-1, you have to be honest and say you settle for that. But the lads wanted something different and showed great drive and determination to get the winner.
"We are past the 30-point mark now, so for us and the team, that is a big confidence booster.
"Kamara is a very good character, very down to earth and is really delighted at the prospect of being at Norwich and in the Premier League.
"We will have to see how he develops, but this is not a particularly tough group to integrate into and he has fitted in very nicely."
Everton boss David Moyes:
"We had controlled the game, but were wasteful in the second half when we had chances to get another goal, and we were always going to be put under pressure at the end.
Moyes annoyed by added time
"I cannot understand why he plays three minutes and 20 seconds for the stoppage time, but he has got that discretion, although I disagree with it.
"We passed it well enough and tried to do the right things, but we were not good enough in the final third - but one thing is for sure, we did not deserve to lose.
"There is still chances for us to do it (get into the top four), but we are going to have to be very good to do it. However, we should have seen this one out, if we have any real ambitions, then we have to make sure we do not lose that game."
Full Time The referee blows for the end of the match.
Assist on the goal came from Sebastien Bassong.
90:00 +3:16 Goal scored
Goal! - Grant Holt - Norwich 2 - 1 Everton Grant Holt fires in a goal from close range high into the middle of the goal. Norwich 2-1 Everton.
Shot from 6 yards from Grant Holt. Sylvain Distin gets a block in. Outswinging corner taken left-footed by Robert Snodgrass, Leon Osman manages to make a clearance.
Inswinging corner taken left-footed by Robert Snodgrass from the right by-line to the near post, clearance by Steven Naismith.
Shot by Kevin Mirallas. Save by Mark Bunn.
Robert Snodgrass challenges Phil Jagielka unfairly and gives away a free kick. Direct free kick taken by Phil Jagielka.
Free kick awarded for a foul by Grant Holt on Leighton Baines. Tim Howard takes the free kick.
Free kick awarded for a foul by Phil Jagielka on Grant Holt. Bradley Johnson takes the free kick.
Foul by Grant Holt on Leon Osman, free kick awarded. Free kick taken by Phil Jagielka.
Substitution Bryan Oviedo replaces Steven Pienaar.
Robert Snodgrass provided the assist for the goal.
83:56 Goal scored
Goal! - Kei Kamara - Norwich 1 - 1 Everton Kei Kamara finds the back of the net with a headed goal from close in. Norwich 1-1 Everton.
Outswinging corner taken by Robert Snodgrass from the left by-line played to the near post,
Steven Pienaar has an effort at goal from just outside the penalty box which goes wide of the left-hand post.
Darron Gibson challenges Robert Snodgrass unfairly and gives away a free kick. Direct free kick taken by Javier Garrido.
Free kick awarded for an unfair challenge on Leon Osman by Bradley Johnson. Phil Jagielka restarts play with the free kick.
Substitution (Everton) makes a substitution, with Kevin Mirallas coming on for Nikica Jelavic.
Javier Garrido takes the free kick.
Substitution (Norwich) makes a substitution, with Anthony Pilkington coming on for Wesley Hoolahan.
Free kick awarded for a foul by Marouane Fellaini on Sebastien Bassong.
Corner taken by Leighton Baines from the right by-line, save by Mark Bunn. Darron Gibson produces a left-footed shot from inside the area that clears the bar.
Kei Kamara has a headed effort at goal from close in which goes wide right of the target.
Wesley Hoolahan gives away a free kick for an unfair challenge on Steven Pienaar. Sylvain Distin takes the free kick.
Free kick awarded for a foul by Russell Martin on Steven Pienaar. Leighton Baines restarts play with the free kick.
Inswinging corner taken by Robert Snodgrass, save made by Tim Howard.
Handball decision goes against Bradley Johnson. Direct free kick taken by Darron Gibson.
Grant Holt challenges Leighton Baines unfairly and gives away a free kick. Tim Howard restarts play with the free kick.
Shot from 12 yards from Kei Kamara. Tim Howard makes a save.
Shot from just outside the area by Marouane Fellaini goes over the bar.
Substitution Kei Kamara on for Luciano Becchio.
Corner taken right-footed by Darron Gibson.
Shot by Leighton Baines from 25 yards. Blocked by Russell Martin. Luciano Becchio challenges Leon Osman unfairly and gives away a free kick. Direct free kick taken by Leighton Baines. Jonathan Howson gives away a free kick for an unfair challenge on Steven Pienaar. Free kick crossed left-footed by Leighton Baines from left wing, Sebastien Bassong manages to make a clearance.
Darron Gibson takes the direct free kick.
Booking Grant Holt receives a yellow card.
Grant Holt challenges Seamus Coleman unfairly and gives away a free kick.
Free kick awarded for a foul by Leighton Baines on Luciano Becchio. Russell Martin takes the free kick.
Free kick awarded for a foul by Grant Holt on Seamus Coleman. Phil Jagielka takes the direct free kick.
The referee blows his whistle to start the second half.
45:00 +1:10 Half time
Half Time The referee calls an end to the first half.
Steven Pienaar takes a inswinging corner to the near post.
Shot by Jonathan Howson from 20 yards. Phil Jagielka manages to make a clearance. Inswinging corner taken left-footed by Robert Snodgrass, Steven Pienaar makes a clearance. Shot by Wesley Hoolahan. Tim Howard makes a comfortable save.
Mark Bunn takes the direct free kick.
Booking Leighton Baines is cautioned.
Leighton Baines challenges Robert Snodgrass unfairly and gives away a free kick.
Corner taken by Steven Pienaar played to the near post, Grant Holt manages to make a clearance.
The assistant referee signals for offside against Nikica Jelavic. Free kick taken by Mark Bunn.
Leighton Baines provided the assist for the goal.
38:46 Goal scored
Goal! - Leon Osman - Norwich 0 - 1 Everton Leon Osman finds the net with a headed goal from inside the six-yard box. Norwich 0-1 Everton.
Free kick awarded for a foul by Jonathan Howson on Marouane Fellaini. Leighton Baines restarts play with the free kick.
Grant Holt takes a shot. Save by Tim Howard.
Seamus Coleman has an effort at goal from outside the area which misses left.
Unfair challenge on Bradley Johnson by Marouane Fellaini results in a free kick. Free kick crossed by Robert Snodgrass, comfortable save by Tim Howard.
Unfair challenge on Robert Snodgrass by Steven Pienaar results in a free kick. Russell Martin restarts play with the free kick.
Russell Martin concedes a free kick for a foul on Steven Pienaar. The free kick is delivered left-footed by Leighton Baines from left channel, Unfair challenge on Russell Martin by Marouane Fellaini results in a free kick. Mark Bunn restarts play with the free kick.
Marouane Fellaini takes a shot from just outside the penalty area which clears the crossbar.
Inswinging corner taken left-footed by Robert Snodgrass, clearance by Sylvain Distin.
Corner taken by Darron Gibson from the left by-line to the near post, Grant Holt manages to make a clearance.
Marouane Fellaini has a drilled shot. Michael Turner gets a block in.
Luciano Becchio challenges Phil Jagielka unfairly and gives away a free kick. Tim Howard takes the free kick.
Marouane Fellaini gives away a free kick for an unfair challenge on Jonathan Howson. Jonathan Howson takes the free kick.
Jonathan Howson takes a shot. Blocked by Grant Holt.
The assistant referee flags for offside against Grant Holt. Sylvain Distin takes the indirect free kick.
Headed effort from inside the area by Nikica Jelavic misses to the left of the goal.
The assistant referee flags for offside against Grant Holt. Free kick taken by Phil Jagielka.
Nikica Jelavic takes a shot. Save by Mark Bunn.
Robert Snodgrass takes a shot. Blocked by Sylvain Distin. Outswinging corner taken left-footed by Robert Snodgrass, Marouane Fellaini makes a clearance.
The referee blows for offside against Nikica Jelavic. Mark Bunn takes the indirect free kick.
Grant Holt fouled by Seamus Coleman, the ref awards a free kick. Javier Garrido takes the direct free kick.
Foul by Javier Garrido on Steven Naismith, free kick awarded. Free kick taken by Phil Jagielka.
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