Teemu Pukki scored his eighth goal of the season to move Norwich up to fourth place in the Championship.
The Finnish striker had not managed a goal in his five previous matches, but scored inside the opening minute as Swansea paid the price for a lacklustre opening after a month’s inactivity.
Pukki netted after just 58 seconds and although Swansea controlled most of the match thereafter, the home side lacked precision and a cutting edge to break down a well-organised Canaries defence.
It was a fifth away victory of the season for manager Dean Smith’s side, while Swansea’s failure means they have not won in six matches and they lie two points adrift of the play-off spots.
Swansea began as if they had not played for 12 months, never mind one.
They gave away possession from the kick-off and should have been 1-0 down inside six seconds after mistakes from Ben Cabango and Joel Latibeaudiere let in Pukki.
The Norwich striker’s shot was blocked for a corner, but he did not have to wait long for the opener as Swansea failed to deal with Gabriel Sara’s inswinging kick and after a flick-on by Kenny McLean, Pukki scored at the far post.
The Swans – who had restored Cabango to their line-up after his World Cup exploits with Wales in Qatar – slowly settled and almost equalised in the 10th minute.
Neat exchanges between Ryan Manning and Luke Cundle opened up the Canaries’ defence but when the cross fell to Joel Piroe, his shot was blocked in a crowded goalmouth.
Swansea continued to dominate possession but some last-ditch tackling from Sam McCallum and Grant Hanley enabled the visitors to protect their lead.
When Norwich countered, Cabango also made a timely block to deny Sara from 12 yards.
Another error from Matt Grimes let in Josh Sargent just before half-time, but the American striker screwed his cross-shot just wide of the far post.
Norwich rode their luck again at the start of the second half, with both Manning and Jamie Paterson unable to convert intricate build-up play into concrete shots on goal.
Swansea head coach Russell Martin sent on two further returnees from the World Cup duty – Wales’ additional squad player Ollie Cooper and Cameroon’s Olivier Ntcham – on the hour mark to add extra zest to their quest for an equaliser.
It almost paid off within five minutes after the pair were involved in a move that ended with Piroe’s downward header bringing a fine save from Norwich goalkeeper Angus Gunn.
Moments later Kyle Naughton flashed a low cross into the Norwich goalmouth, but Piroe was inches away from the crucial touch.
Joe Allen made it a fourth Swans player to return to club action from Qatar when the Wales midfielder came on a 71st-minute substitute.
But his arrival could not inspire Swansea, who were easily blunted in the final minutes to enable Norwich to claim the points.
