Having coming from behind to lead Swansea, the Canaries failed to hold on for what would have been a valuable victory in their quest to confirm their Premiership place for next season.
Mark Bunn appeared to injure himself in dealing with a difficult back pass and was forced to make way for Lee Camp with only fifteen minutes on the clock.
For the first half hour the visitors passed the ball better than the home side on a less than perfect Carrow Road pitch and it came as no great surprise when their top scorer, Michu put them ahead with a rasping shot into the roof of the net when the ball was pulled back into his path by Jonathan de Guzman.
After forty minutes, Elliott Bennett delivered an excellent cross from the right wing after being released by the hard-working Kei Kamara, and his fellow winger, Robert Snodgrass equalised with a well placed diving header at the far post.
HALF-TIME: City 1 Swansea 1
The second half saw the Canaries playing more like the team that amassed 25 points before Christmas and when Michael Turner stabbed home Bennett's free kick from the right wing at the far post it began to look as if they were on course for a much needed three points.
In fact there were opportunities for a third goal, with Kamara coming the closest to scoring when the ball was nicked off his toe by Ashley Williams as he was poised to tap in a low cross from the left by Snodgrass.
The missed chances proved costly, because with a quarter of an hour of normal time remaining, substitute Angel Rangel broke free on the Swansea right and his cross enabled Luke Moore to beat Camp from close range.
From that point on the game could have gone either way with the best chance falling to Michu who was unable to add to his impressive goal tally of 21 goals this season. Costing just £2 million, the Spaniard is undoubtedly the bargain buy of the season and his addition to the team is the most likely reason why Swansea go into the last six games of the season six points ahead of Norwich...
FULL-TIME: City 2 Swansea 2