The Canaries were out of luck, seeing the woodwork rescue Tottenham twice in the first hour and had two other efforts cleared off the time well before the visitors threatened the home goal.
If that was not bad enough, City had lost three players through injury by the start of the second half.
By that time Martin Jol's interval instructions had set the stage for Spurs to claim a fifth successive victory.
The visitors kicked off attacking the Barclay End goal. Timothee Atouba put in a useful left-wing cross but it eluded everyone and went out for a throw-in.
At the other end a David Bentley cross was gathered by Paul Robinson. Norwich were then forced to make an early substitution when Simon Charlton limped off with a dead leg to be replaced at left-back by Adam Drury.
Darren Huckerby set up Bentley, but his shot came back off a post with Robinson well beaten.
This lifted home players and fans alike in the 14th minute Mattias Jonson got in a fierce drive which just cleared the Spurs crossbar and Bentley saw his shot beat away by Robinson.
Frederic Kanoute was put through by Robbie keen but he fired over.
Michael Brown was lucky to escape a booking when he tripped Huckerby inches outside the Spurs penalty area.
Huckerby's free-kick was headed goalward by former Spur Gary Doherty, but Pedro Mendes cleared the ball off the line with a firm header.
In the 27 minute Johnson's lay-off gave Bentley a chance but his snap-shot cleared the bar.
At the other end Kanoute was dispossessed inside the City's six-yard box, but Youssef Safri sprained his ankle in the process.
Minutes before half-time Jonson left the field with concussion to be replaced by Paul McVeigh.
Bentley picked out Leon McKenzie with a right-wing cross, but he tried to control the ball and the shooting chance was lost.
Safri was booked for a foul on Mendes and in stoppage time McKenzie was denied by Noureddine Naybet's goal-line clearance after he had beaten Robinson to Huckerby's through ball.
Phillip Mulryne replaced the injured Safri at half-time.
Norwich were unlucky seven minutes into the second half when Huckerby's left-wing corner found McKenzie, but his header appeared to be touched on to the cross by Robinson's outstretched fingertips.
From the breakaway Spurs almost scored but Green did well to gather Robbie Keane's pass before it reached Kanoute.
Spurs then enjoyed their best spell and Mendes brought an acrobatic save from Green with a snapshot.
Reto Ziegler replaced Atouba after 64 minutes. Seven minutes later Kanoute made way for Jermain Defoe.
In the 73rd minute, with most people expecting a goal-kick, the referee awarded a corner to Spurs and when Norwich failed to clear the right-wing flag-kick from Mendes, Drury's half-hit clearance fell to Keane, who gave Green no chance with a fierce left-foot shot from ten yards.
Brown then put a broad smile on his manager's face when he collected a pass from Keane and beat Green high to his left with a 25-yard right-foot shot.
McKenzie headed over from Huckerbys corner and Green kept out of shot with Defoe with his legs.
In the dying seconds Thomas Helveg's shot was saved by Robinson and Doherty headed over, proving that it definitely was not City's day.