City extended their unbeaten run to seven games as Sebastien Bassong's first goal of the season clinched a last gasp 1-1 draw at Everton.
The Toffees had taken an early lead through Steven Naismith with an 11th minute strike and although the home side had the better of the first half it proved a game with very few clear cut opportunities for either side.
City were more purposeful in the second half and went in search of the leveller and although Anthony Pilkington pulled two saves from Tim Howard in the Everton goal, it was left for Bassong in the 90th minute to rise and meet an excellent Javier Garrido free-kick to head it past the American and break Everton hearts.
Norwich Manager Chris Hughton commented after the game: "I'm pleased for a number of reasons. I didn't think that was one of our better performances.
"It's a really spirited squad and when we were one behind we kept pushing and pushing for an equaliser. It's a game of chances and I'm delighted that we took ours at the end."
The Canaries had one inforced change in defence, with Michael Turner sidelined with a shoulder injury Ryan Bennett came into the starting line-up. The rest of the squad remained the same from City's previous four games including last week's 1-0 victory over Manchester United at Carrow Road.
Everton had some key players missing from their team, including Marouane Fellaini and Phil Neville through suspension and injury respectively.
The hosts created a good opening as early as the second minute when Steven Naismith laid the ball off for Leon Osman who's turn and shot on the edge of the box just curled past the far post to safety.
And although the opening 10 minutes were fairly even in terms of possession it was Everton who took the lead on 11 minutes. Bryan Oviedo capitalised on an error by Steven Whittaker, cutting the ball back for Naismith to hit home high into the roof of the net for 1-0.
It was just five minutes later when Leighton Baines pushed forward and had a shot parried by Ruddy, the ball falling to Osman but he could only hit his shot into the ground and over the bar to the relief of the Canaries.
The Toffees were starting to get on top - Baines again with a burst into the area before delivering a dangerous cross which just went over the head of Nikica Jelavic in the six-yard box.
City were trying to build possession through midfield but both Holt and Hoolahan were found in offside positions in the final third, but City's best opening came on 25 minutes, Grant Holt bursting through the middle and riding a challenge before hitting a shot wayward of Tim Howard's goal.
Just after the half hour mark Osman had another shooting chance but it was straight at former Everton man Ruddy. Naismith also pulled another stop from the City stopper a couple of moments later after beating offside.
With five minutes of the first half left City worked themselves a corner after some good build-up play - Bassong heading wide from Snodgrass' delivery.
The Canaries were having the better of the closing minutes and Holt and Hoolahan linked up well, but as the Irishman looked to play a neat one-two with Snodgrass the Scot was deemed in an offside position.
The first period ended with a free-kick to the Canaries far right, but referee Mike Jones felt there was pushing in the box as people fought to get on the end of Robert Snodgrass' delivery and Everton were awarded a free-kick.
Half-time: Everton 1, Norwich City 0
The opening five minutes saw the Canaries venture forward and win a free-kick - again a Snodgrass curling delivery, which was initially cleared only to Alex Tettey who controlled and had a dig, but unfortunately it was off target.
City's best chance so far came from another set piece on 57 minutes - Hoolahan winning the free-kick and Anthony Pilkington stepping up with a curling effort which Howard had to parry and collect on the second attempt.
Then a minute later Holt evaded the offside flag and made a run in on goal, but Howard rushed out narrowing his space and did enough to block City's number nine from lobbing the ball over him.
City kept up the pressure as some good link up play between Hoolahan and Pilkington put the Canaries in behind Everton, but the winger's cross just fell behind Snodgrass forcing him to miss Tettey with the pass, and allowing the home side to clear their lines.
Everton remained a threat however with City pushing forward - Leighton Baines made a powerful run forward before sternly testing Ruddy with a shot, the England man doing brilliantly to make the save.
The Canaries made a change on 75 minutes, Steve Morison replacing Hoolahan and City were forced into another substitution just five minutes later when John Ruddy
seemed to be struggling with a knock - Mark Bunn replacing him for his first Premier League appearance for the Canaries.
City kept up the pressure however and on 85 minutes Whittaker found Pilkington with a good cross but again Howard kept his side in front with an important save.
One last throw of the dice from manager Chris Hughton saw Simeon Jackson replace Snodgrass.
And at the death City's persistance paid off - Morison won a free-kick and with Snodgrass having just been susbstituted, Javier Garrido delivered a deep free-kick to the far post and it was Sebastien Bassiong who rose high to head the Canaries level to the delight of the Canary faithful on the far side.
With four minutes of injury time announced David Moyes' made his first change of the game Naismith coming off for Apostolos Vellios, but City saw out the rest of the game to claim the point and extend their unbeaten run.