However, 15 minutes into the game Norwich looked to be heading for a much-needed three points thanks to goals from Dean Ashton and Leon McKenzie.
Unfortunately their defence fell asleep after 25 minutes allowing Antoine Sibierski to pull a goal back and, 12 minutes later, Robbie Fowler notched up his 150th Premier League goal to make it all square, when Shaun Wright-Phillips set him up with a low cross.
Things got worse for the home side with a second yellow card for Mattias Jonson. Even then the hardworking McKenzie created an opening with a low cross, but none of his colleagues were in a position to complete the move.
Just when it looked as if Norwich had done enough to earn a point, Fowler grabbed an injury-time winner.
The visitors kicked off attacking the River End goal and Kiki Musampa had an early chance, but fired into the side netting.
McKenzie and Jonson got in each other's way when Graham Stuart put in an inviting cross from the right after good control by Ashton, before Damien Francis got into a good position but shot tamely at David James.
Ashton put Norwich in front after 12 minutes when he volleyed Adam Drury's throughball inside David James' left hand post with the outside of his right foot from some ten yards.
McKenzie made it 2-0 three minutes later. He exchanged passes with Ashton before racing clear of the Citizens defence. He then calmly slid a left foot shot past James.
Sibierski wasted a good chance when he chipped the ball over the bar with only Robert Green to beat as the visitors tried to fight back.
Wright-Phillips forced Green to make a save with a low shot, then Sibierski made up for his earlier miss when he glanced a header past Green at the far post from Musampa's right wing cross.
With Gary Holt on his knees clutching a head wound referee Rob Styles allowed play to continue, to the annoyance of the Norwich players, and Wright-Phillips outsmarted Jason Shackell on the left of the penalty area to set up Fowler, who met his low cross with a firm finish from eight yards.
Holt was able to return with a well-bandaged head before half-time.
Incredibly the second half continued at the same hectic pace as the first 45 minutes, but without the goals. Joey Barton and Jonson were booked for fouls and in the 67th minute Jonson's rash challenge earned him a second yellow.
Down to ten men, the Canaries still had chances and James did well to keep out a fierce drive from Ashton.
The only substitution of the game came when Youssef Safri replaced Stuart after 75 minutes.
Barton brought a save from Green with a low drive and Fowler fired wide as the ten men struggled to get out of their own half.
A determined run by McKenzie ended with a low cross but there was no Norwich player on hand to finish the move.
Just when it looked as if Norwich had earned a precious point, Green could only block a Wright-Phillips cross from the right and when it fell to Fowler his half-hit shot from four yards trickled inside the far post to send Manchester City home with all three points.