A Borja Sainz goal five minutes from time condemned the Sky Blues to defeat at Carrow Road.
City took the lead at the start of the second half, when Callum O’Hare scored his seventh goal of the season.
However, the Canaries would level through Josh Sargent and then after Liam Kitching was shown a red card, Sainz capitalised with a winner late on.
The Sky Blues started on the front foot and were applying the pressure to the Norwich back four and successfully, with Milan van Ewjk winning the ball back and finding Callum O’Hare, who looked for Haji Wright in the middle, but he was unable to get a shot away.
At the other end, space opened up for Christian Fassnacht on the edge of the area, but Brad Collins was equal to it, making a fine stop to his right.
Victor Torp was making his first league start for City and he picked out Wright with a neat through ball and from a tight angle, the striker flashed a shot wide of goal.
The striker was back in the team after recovering from a calf injury he picked up against Middlesbrough and he was causing the hosts problems, firing another shot in towards the near post and this time Gunn had to make the save to keep out his strike.
Torp was the next to try and test Gunn in the Norwich goal, unleashing a fierce effort from range which whistled over the bar.
HALF-TIME: Norwich City 0-0 Sky Blues
It was the perfect start for City in the second half, as they latched onto a mistake at the back in the Norwich half and Victor Torp found O’Hare and he beat his man in the area and slotted the ball into the bottom corner to make it 1-0.
It was so close to being 2-0 minutes later and this time it was O’Hare who turned provider, picking out Haji Wright and he charged into the box and was only denied by an excellent stop from Angus Gunn.
However, the Canaries would pull level on the hour mark, and it was Josh Sargent who fired in on the half-volley from inside of the area.
The game took a turn ten minutes later, as the Sky Blues were reduced to ten men when Liam Kitching was shown a red card.
From the resulting free-kick, Gabriel Sara rattled the top of the woodwork, as his shot hit the bar and went behind for a goal-kick.
City introduced Kasey Palmer with 15 minutes remaining and he almost produced a moment of magic, fending off his marker, before firing a shot at goal, which Gunn saved well.
Norwich put themselves in front with five minutes remaining when Borja Sainz fired in from the edge of the area.
FULL-TIME: Norwich City 2-1 Sky Blues
Goals: Callum O’Hare 48’, Josh Sargent 60’, Borja Sainz 85’
Yellows: Marcelino Nunez, Dimitris Giannoulis
Reds: Liam Kitching
Attendance: 26,306 (1,870)
Starting Xl: Brad Collins (GK); Milan van Ewijk, Bobby Thomas, Liam Kitching, Jake Bidwell (Dasilva 69’); Victor Torp (Eccles 69’), Jamie Allen, Callum O'Hare (Godden 90'); Tatsuhiro Sakamoto (Binks 74’), Ellis Simms (Palmer 74’), Haji Wright.
Unused Subs: Ben Wilson (GK), Joel Latibeaudiere, Liam Kelly, Fábio Tavares, Matty Godden.
Starting Xl: Angus Gunn (GK); Jack Stacey, Ben Gibson, Shane Duffy, Dimitris Giannoulis, Christian Fassnacht, Gabriel Sara, Kenny McLean (C), Marcelino Nunez, Borja Sainz, Josh Sargent.
Unused Subs: George Long (GK), Grant Hanley, Liam Gibbs, Ashley Barnes, Sydney Van Hooijdonk, Sam McCallum, Jacob Sorensen, Onel Hernandez, Kellen Fisher.