The Canaries extended the points gap between themselves and Sheffield United to seven points with this hard won victory.
The Blades played some neat passing without finding a way to cut through the City defence.
The only goal of the game came via veteran striker Iwan Roberts just before the hour when he capitalised on a good run and cross from Darren Huckerby and pounced when the Sheffield defence failed to clear the danger.
The home side kicked off attacking the Barclay end goal but made little headway against a solid Blades' defence.
In the 20th minute Nick Montgomery came close to breaking the deadlock as his shot went inches wide of Robert Green's right hand post.
Three minutes later Huckerby appeared to be tripped in the visitors' penalty area but referee Knight was unmoved by his appeal.
Within seconds Jim Brennan went down but once again the ref was unimpressed.
Brennan then produced the first shot on target of a game which had seen few chances, but it hit one of his own players and was cleared to safety.
Paddy Kenny played a sweeper's role on several occasions in the first half and just before the break he was caught late by Huckerby as he raced to clear the ball near the touchline. The City player became the only booking of the game.
In the 14th minute of the second half Huckerby stepped up a gear, beat his marker, and delivered a low cross from the left. When it was only half cleared, Roberts volleyed home with his left foot from some 12 yards out.
Five minutes later Wayne Ellison fired wide from five yards while at the other end Roberts headed straight at Kenny when he looked certain to double the score.
The keeper was given much more to do when Mark Edworthy's right-wing cross was deflected Goalwards by Phil Jagielka.
In the 73rd minute Paul McVeigh cut in from the right wing but his shot flashed past Kenny's right hand post.
Paul Peschisolido replaced veteran Stuart McCall and Dean Sturridge came on for Paul Shaw.
Norwich replaced Damian Francis with Phil Mulryne and the Irishman could have rapped it up for City within seconds of his arrival but fired over after good work by Roberts, Huckerby and McVeigh.