Gary Hooper had a goal ruled out for offside in the first half while Manuel Pellegrini's men hit the bar as Chris Hughton's side effectively kept a lid on the title contender.
Manuel Pellegrini's previously free-scoring side – which last month reached 100 goals in all competitions faster than any team in the Premier League era - has run into unforeseen problems in the last two outings, losing the Premier League's top spot to Chelsea in the process.
A 1-0 loss at home to Jose Mourinho's side on Monday was compounded by another lackluster display at Carrow Road – the absence of Brazilian midfielder Fernandinho due to a muscle strain once again keenly felt.
Alvaro Negredo headed a first-half corner against the crossbar but clear chances were in short supply as Norwich claimed an unexpected point in the fight for top-flight survival.
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On-loan Fenerbahce defender Joseph Yobo made his Norwich debut as a thigh injury ruled out Ryan Bennett.
James Milner returned from a groin complaint to bolster the City's injury-hit midfield, while Stevan Jovetic got the nod over Edin Dzeko to make his second Premier League start of the season in attack.
A prone Yobo scrambled the ball to safety as playmaker David Silva appeared poised to convert Gael Clichy's early cross for Pellegrin's men, but the recalled France fullback was caught out in the 16th minute.
Norwich winger Nathan Redmond burst into the box when Clichy failed to cut out Gary Hooper's pass but blazed high and wide.
Hooper had the ball in the net two minutes later but was lurking in an offside position after Joe Hart parried Leroy Fer's header from a Redmond corner.
Manchester City came close from a similar dead-ball situation in the 36th minute – Negredo heading onto the crossbar following a Martin Demichelis flick-on from Jesus Navas' delivery.
Negredo crashed a rasping long-ranger into the side netting and, by the time John Ruddy kept out a stinging 20-yard strike from Jovetic in the 43rd minute, Pellegrini's charges were showing signs of hitting their stride.
Their customary rhythm remained largely elusive as the second half got under way, but Norwich fullback Martin Olsson produced an excellent last-ditch challenge to thwart Navas.
Russell Martin then positioned himself well to stop Jovetic converting Milner's looping right-wing cross.
Ricky van Wolfswinkel arrived from the bench after 68 minutes in place of Hooper, who hobbled away from a robust Milner challenge, but Norwich had faded as an attacking force by that point, though the club's excellent organization continued to confound City..
Dzeko, on for Jovetic, pulled a shot into the side netting at the end of another fruitless attack and Pellegrini was left to rue a golden opportunity missed, while Van Wolfswinkel and Anthony Pilkington were both agonizingly close to handing Norwich an unlikely triumph.