Demba Ba scored his third goal in two games to spoil Norwich manager Chris Hughton's return to Newcastle.
Ba scored twice after coming on as a substitute against Everton on Monday, and he marked his return to the starting line-up by converting Hatem Ben Arfa's defence-splitting pass.
Papiss Cisse could not add to Ba's goal when he missed a first-half penalty.
Wes Hoolahan and Andrew Surman wasted chances for Norwich, who have yet to win in the league this season.
It was a deserved victory for Newcastle, who should have won more convincingly, while Hughton, who was sacked as Magpies manager in December 2010 despite leading them to promotion months earlier, will be concerned by his side's ongoing problems in front of goal.
The Canaries, who lost defender Sebastien Bassong to a hamstring injury after just six minutes, did create some decent chances but their composure was missing - something that cannot be said about Ba at the moment.
The 27-year-old striker, whose agent upset manager Alan Pardew with comments suggesting Ba may want a move away from Newcastle, scored against the run of play with a well-worked goal which was direct in definition but exquisite in its execution.
Goalkeeper Steve Harper, deputising for the injured Tim Krul, rolled the ball out to Ben Arfa who glided forward before splitting the Norwich defence with a sublime pass which Ba latched onto and, with his second touch, clinically placed the ball past John Ruddy and into the back of the net.
The goal summed up much of Newcastle's play, with Ben Arfa regularly picking the ball up in the deep and causing the Canaries defence problems with his mixture of inch-perfect passing and mazy dribbling.
The French midfielder almost set up Ba and Cisse on two other occasions - with the Senegalese pair experiencing contrasting fortunes.
While Ba appeared to be buoyed by his strike, his partner is now without a goal in six matches this season.
And his effort for the penalty, won when Mike Williamson was backed into and knocked over by Steve Morison, summed up his day - the ball never threatening the goal as it soared high into the stand.
Hughton's decision to bring in Hoolahan and Morison to replace Grant Holt and Simeon Jackson did not bear dividends, and the Canaries have now scored only twice in five Premier League matches.
Left-back Javier Garrido was their best attacking option, with the former Manchester City man creating two useful chances for Hoolahan and Robert Snodgrass, but they struggled to assert themselves after they had fallen behind.
Their best chance came at the beginning of the second half when Harper denied Andrew Surman after the midfielder had been put clean through on goal.
Hughton sent on Holt and Jackson, but it was the hosts who looked more threatening in the final stages as Ba was put through by Cabaye and saw his shot saved by Ruddy before the keeper denied Gabriel Obertan in stoppage time.
Victory moves Newcastle up to 10th in the Premier League table while Norwich, who face Liverpool, Chelsea and Arsenal in their next three league games, remain just above the relegation zone.