Watford, on the other hand, seemed to have been stung into action by Saturday's defeat at home by the Baggies and were 2-0 up by half-time.
In fact they looked well in command for most of the game, except for a few minutes when City managed to pull a goal back 20 minutes into the second half.
The home side kicked off taking the River End goal and won the first corner of the game in the eighth minute.
The first booking came four minutes later for Gavin Mahon's foul on Darel Russell.
David Marshall was forced to tip Tommy Smith's inswinging cross over the bar, then the Norwich keeper had to get down smartly to save Marlon King's low drive.
After half an hour Jamie Cureton managed a first shot for the home side, but it cleared the crossbar.
The Championship leaders went ahead after 36 minutes when Lloyd Doyley's low right-wing cross was turned into the net from close range by Darius Henderson.
It became 2-0 after 42 minutes when Adrian Mariappa headed Adam Johnson's left-wing corner against the near post and Marshall saw the ball rebound into the net off his legs.
Glenn Roeder made a double substitution nine minutes into the second half, Lee Croft and Chris Martin replacing Jimmy Smith and John Hartson.
On 65 minutes Martin took a quick throw-in and Cureton squared the ball from the left and it was turned in at the near post by Croft.
With Watford seeming happy to run the clock down, Croft was dispossessed deep in his own half by Lee Williamson who fed the ball through to King.
His cool finish with a right-foot angled drive killed off the game two minutes from full-time.