Not for the first time this season City fell behind when an attacking move broke down. True to recent form they also conceded a second very shortly afterwards.
To their credit they did not give up and when substitute Ryan Jarvis pulled a goal back near the end the Reds had to hang on rather desperately to get all three points.
Norwich kicked off attacking the River End but it was the visitors who forced the first corner of the game, after five minutes, when Simon Charlton created problems for his own defenders by giving the ball away deep in his own half.
Norwich were forced to play for a few minutes with ten men while Mattias Jonson had to leave the field of play to have stitches in head wound. He was able to continue with a well bandaged head.
He was presented with a shooting chance by Darren Huckerby but gave no problem to Liverpool goal keeper Jerzy Dudek with an half-hit shot
In the 25th minute Steven Gerrard put plenty of power into his rasping drive, but it went wide
Five minutes later John Arne Riise fired wide when well positioned inside the Norwich penalty area.
A Gerrard free-kick was blocked and the same thing happened to one from Riise.
Damien Francis was booked for a challenge Sami Hyypia, but referee Howard Webb took a more lenient view when Hyypia flattened Leon McKenzie three minutes before half-time.
In stoppage time Luis Garcia fired high into the Barclay Stand.
A minute into the second half a throughball from Phil Mulryne was just too long for McKenzie and Gary Doherty achieved the same result with his lofted pass.
Steve Finnan was booked for foul on Huckerby in the 53rd minute.
Huckerby's left-wing cross was then handled by Jamie Carragher, but Norwich had to settle for another corner.
With City throwing men forward Liverpool scored on the break. Riise found Garcia with a throughball from left to right and the Spaniard's first time right-foot effort from 16 yards cleared the advancing Robert Green before bouncing into the roof of the net.
Hyypia was then booked for foul on McKenzie before Neil Mellor was replaced by Florent Sinama Pongolle and within seconds he had played a part in his side's second goal.
He blocked Craig Fleming's attempted clearance with his chest and although his shot was palmed away by Green, it fell invitingly to Riise on the six-yard line and he smashed the ball into the unguided net with a left-foot shot.
Norwich made a double substitution when McKenzie and Mulryne made way for young Danny Crow, making his Carrow Road debut, and Jim Brennan.
Antonio Nunez made way for Dietmar Hamann and Francis was replaced by Jarvis, who found the net five minutes from full-time.
He collected Jonson's cross from the left and controlled the ball on the edge of the 18-yard box before beating Dudek high to his right with a firm left-foot shot.