Everton paid the ultimate price for three barmy minutes at Carrow Road, despite Richarlison coming off the bench to score with a tremendous bicycle-kick strike.
The Brazilian forward, who was sent on by Rafa Benitez alongside Yerry Mina with 36 minutes remaining and Everton trailing 2-0, struck on the hour to set up a closing period that resembled an attack-v-defence exercise.
But despite setting up camp in the hosts' half, and with Richarlison, Anthony Gordon and Demarai Gray taking the fight to Norwich, Everton couldn’t muster an equaliser.
The away side fell behind when Michael Keane turned Josh Sargent’s low cross into his own net after 16 minutes.
And just 120 seconds later, Adam Idah burst into space in Everton’s penalty area to put clear distance between the teams.
The announcement of seven minutes of added time sent anxious an cry rolling around the stadium.
But despite maintaining pressure on the home goal throughout stoppage time, Everton had given themselves too much ground to recover. Indeed, Milos Rashica dribbled a shot onto the post with the last kick of the game as the away side committed bodies to attack.
Everton had looked relatively untroubled when Norwich stole a significant march on the visitors shortly after the quarter-hour mark.
The first goal owed a little to a slice of fortune in favour of the home team. Sargent and Max Aarons traded passes on the right but seemed out of ideas when Sargent eventually slid in a low cross.
Teemu Pukki was lurking but Everton had the situation in hand, Keane covering the front post and Ben Godfrey monitoring his former teammate in the middle.
Keane, though, instinctively jabbed out his left boot, rerouting the ball and completely wrong-footing Jordan Pickford, who was defeated low to his left.
Pickford had been unemployed until that point, other than a straightforward stop down to his right after a Keane clearance fell for Pierre Lees-Melou to take aim from 25 yards,
Gray was making things happen for Everton from early on, the winger repeatedly attracting illegal attention from defenders struggling to get to grips with the pace and direct dribbling of a player high on confidence.
Tim Krul’s handling was sure when Gray unleashed a snapshot on 15 minutes and there was very little to indicate what was about to unfold.
But following Keane’s unfortunate intervention, Norwich came again.
Brandon Williams seized on a loose ball on the home team's left to swarm forwards. As he reached Everton’s defensive third, the left-back, on loan from Manchester United, looked up to see Idah’s run bisecting Keane and Vitalii Mykolenko.
The pass was squeezed through a narrow corridor perfect for Idah. The striker had to reach for his second touch but managed to prod the ball beyond Pickford.
Dominic Calvert-Lewin and Salomon Rondon were paired up front for Everton, although the two strikers began the game by taking it in turns to head Rashica free-kicks out of their own penalty area.
Everton, though, evidently wanted to work the ball wide for the quick-witted duo of Gray and Gordon, to supply their imposing centre-forwards with regular service.
Grant Hanley tried to rough up Gray inside two minutes but it’ll take more than a buffeting from a grizzled centre-back to deter the Everton player.
Gray picked himself up after being fouled by Lees-Melou following a brisk Everton counter-attack to strike a free-kick into the wall at 0-0.
He was prominent again as Everton steadily regained their composure following the hosts’ double whammy.
There was a wicked, dipping cross right before half-time, which Williams did very well to defend with Calvert-Lewin seeking to convert.
Hanley made a similar intervention to frustrate the same Everton player after another inviting delivery from the left. Abdoulaye Doucoure picked up the seconds from that one, the Frenchman’s low shot clattering into a defensive body. Gordon’s subsequent attempt at a cross was diverted behind.
Norwich were stretched but just about keeping Everton at arm’s length.
Krul heaved a huge sigh of relief after shovelling a vicious Gray corner around the near post and soon after the Norwich goalkeeper was alert to prevent Calvert-Lewin fastening onto a Rondon flick.
Everton’s best passage of play in the opening half? That came on 34 minutes. Gordon roamed infield, keen to take responsibility and swerving challenges, before linking with Gray.
The ball was worked back in the other direction – left to right – shuffled through Andre Gomes and Doucoure, to Seamus Coleman.
The cross arrived behind Rondon, who swivelled to volley but couldn’t gain sufficient purchase to extend Krul beyond a routine stop.
Pickford watched Lees-Melou’s meaty strike from distance all the way into his midriff shortly after the restart.
A let off for Everton followed in short order. Mykolenko was oblivious to the presence of Idah when the left-back turned a pass in the direction of Pickford.
Idah couldn’t take advantage, a heavy first touch allowing Godfrey to steal in and clear.
Benitez dipped into his replacements, Richarlison and Mina replacing Coleman and Godfrey.
And the changes took tangible effect only six minutes later.
Hanley headed out Gray’s right-wing corner but Mykolenko was in position to hoover up possession on the opposite side.
The player making his Premier League debut sent in a teasing cross. It needed dealing with by Krul, who was surrounded by bodies and had no option but to punch.
The ball travelled over the head of Richarlison, who adjusted and contorted his body to execute an exquisite overhead kick. Krul had no chance and Lees-Melou on the line would have needed to add another foot to his angular frame to prevent the goal.
Norwich profited from a stroke of luck as Everton put their foot down in pursuit of a leveller.
Ben Gibson tried to swipe clear a Gomes set-piece but was alarmed to see the ball slam into the back of defensive partner Hanley and rebound towards goal. It was Krul, though, who got the break, rather than Calvert-Lewin, about one yard away.
The mobile Richarlison drilled a right footer into the frame of Hanley before Everton looked poised for an equaliser on 83 minutes.
Gomes ushered in Gray for a cross that appeared destined to run into touch until Godfrey – now operating at right-back – hooked a boot around the ball.
It rolled back to Gordon whose shot was on target but blocked by substitute Dimitris Giannoulis.
Krul dived to his right to hold an effort from Godfrey, while Mina blocked a low Idah blast following a Norwich break deep into seven minutes of added time.
And in the final passage of play, Rashica sped down the left and clipped his low effort against the far post.