The Swans suffered a second consecutive defeat as Wes Hoolahan's 70th-minute header settled this encounter at Carrow Road.
The Norwich midfielder headed home from close range after sub Dieumerci Mbokani directed a deep corner back into his path.
The Swans failed to carve open a promising opportunity during a frustrating afternoon in East Anglia.
The result proved Norwich's first win in seven, with the Swans sliding down to 14th with Garry Monk's side still on 13 points from 12 games.
The Swans remained unchanged for a third successive game as Garry Monk kept faith with the team that were beaten at home by Arsenal last time out
Kyle Naughton faced the club where he spent a season-long loan in 2011-12 while the only change in the matchday squad saw Wayne Routledge make his return from a calf injury as Modou Barrow missed out.
Norwich were without captain Russell Martin as he served his suspension following his sending off at Manchester City while Matt Jarvis was sidelined with a knee injury.
Andre Wisdom returned from injury while loan signing Dieumerci Mbokani was among the substitutes after recovering from illness.
John Ruddy, Andre Wisdom, Ryan Bennett, Sebastien Bassong, Martin Olsson, Jonny Howson, Alex Tettey (capt), Gary O'Neil, Robbie Brady, Wes Hoolahan (Youssouf Mulumbu, 90), Cameron Jerome (Dieumerci Mbokani, 68).
Declan Rudd, Steven Whittaker, Graham Dorrans, Kyle Lafferty, Vadis Odjidja-Ofoe.
Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Ki Sung-Yueng, Jonjo Shelvey (Eder, 87), Gylfi Sigurdsson (Leon Britton, 78), Andre Ayew, Jefferson Montero (Wayne Routledge, 64), Bafe Gomis.
Kristoffer Nordfeldt, Angel Rangel, Kyle Bartley, Jack Cork.
It proved a first half of plenty of possession but no real chances for the Swans.
Garry Monk's side were on the ball for the majority of the opening 45 minutes, but their patient approach failed to carve open the home defence.
Norwich had the best chance after nine minutes as Robbie Brady's free-kick found the unmarked Cameron Jerome, but he wastefully headed over from ten yards.
Lukasz Fabianski then had to deal with a tame 25-yarder from Jonny Howson as Norwich looked to make the most of their possession.
At the other end, the best opportunity the Swans could create came via Neil Taylor, with the left-back's curling cross meeting Bafe Gomis, but he volleyed well wide.
That was the last real action of the half, with neither team finding a breakthrough.
HALF-TIME: Norwich City 0 Swans 0
The game opened up slightly in the second half with Brady seeing his header expertly kept out by Fabianski's diving save.
Then sub Wayne Routledge crossed for Gylfi Sigurdsson, but his effort bounced back off the crossbar.
Sigurdsson then turned provider as he touched through for Ki Sung-Yueng, but he scuffed his effort well wide from the edge of the box.
At the other end, Fabianski again had to be at his best to tip wide a fierce drive from Brady.
Then came the breakthrough from the resulting corner, with sub Dieumerci Mbokani - on the field for less than three minutes - nodding across for Howson, who headed through the legs of Sigurdsson from two yards out.
Norwich raised their game a level, and Wes Hoolahan went close to doubling their advantage with a 25-yard effort, but Fabianski tipped it over the crossbar.
Garry Monk made a second change as Leon Britton replaced Sigurdsson for the remaining 12 minutes.
The Swans pushed for an equaliser, with Routledge's low drive flashing wide of the far post while Gomis met a Shelvey cross but he couldn't get his header on target.
That proved Shelvey's final act as he was replaced by Eder for the remaining few minutes.