Match ends, Swansea City 1, Norwich City 0.
Swansea City moved nine points clear of the Premier League relegation zone as Norwich slipped further into danger.
Gylfi Sigurdsson's neat finish into the bottom corner was enough to settle a cagey, low quality match.
Nathan Redmond shot wide late on for the visitors but Swansea, whose head coach Francesco Guidolin missed the game through illness, held on to win.
Norwich remain in the relegation zone and are without a win in 10 matches in all competitions.
Alex Neil's side are now one point from safety after Sunderland picked up a draw against Southampton.
Swansea have now secured back-to-back league victories after their shock win over Arsenal on Wednesday.
A lack of quality
Except for a low Cameron Jerome effort from range that was palmed away by Lukasz Fabianski, neither goalkeeper was tested in an uneventful first half.
But Iceland midfielder Sigurdsson opened the game up shortly after the break with a calm finish that gave Swansea what was, in the end, a deserved win.
He was also denied a second goal from a curling free kick late on by John Ruddy's finger-tip save.
Norwich lacked urgency until the closing stages and pressed late on in the game, but Dieumerci Mbokani could not keep a header down and substitute Patrick Bamford saw a low effort saved.
The Canaries remain without an away win since beating Manchester United in December.
Had you Fer-gotten me?
The second-half introduction of former Norwich midfielder Leroy Fer, signed by Swansea in the January transfer window, gave the hosts a fresh impetus in attack.
It was his square ball that found Sigurdsson in space for the winning goal and, having impressed at the Emirates against Arsenal on Wednesday, he went on to put in a lively performance for the Swans.
Guidolin on the mend
Swansea boss Guidolin picked the team from his hospital bed for a second consecutive game, as he continues to recover from a chest infection.
Coach Alan Curtis, who has taken on first-team duties in his absence, confirmed Guidolin is due to return to work this week and said picking up six points from two games would no doubt aid his recovery.
"I know he's delighted and has sent his best wishes," said Curtis. "He'll probably be relaxing now and it's a huge boost for him.
"He's due to leave hospital on Monday. We won't see him for a couple of days, but I expect him to be at the Bournemouth game next Saturday."
Man of the match: Gylfi Sigurdsson
The stats you need to know
- Norwich City are still the only team yet to keep a clean sheet in a Premier League away game this season.
- The Canaries have kept the joint-fewest clean sheets in the Premier League this season (three, along with Sunderland).
- Swansea have won two successive Premier League games for the only the second time since May 2015.
- The Swans have scored in nine of their 10 Premier League games in 2016.
Swansea coach Alan Curtis: "It was a strange game. The first half was poor from both teams but we upped our game and we got the goal. We were hanging on a bit at the end.
"When it's two teams who need the points it affects it. It was one of the worst games of the season.
"We felt like we had to make changes in the second half and everyone played their part and we're delighted. It gives us breathing space."
Norwich manager Alex Neil: "It was edgy but I don't think there was a team that was clear. You hope you've got the players to make the difference.
"Swansea opened up in a 10-minute spell and got the goal.
"We need to win games to stay in this league. We've got to stay positive and we've got to believe we can win these remaining games. The other teams may determine out fate."
Swansea travel to Bournemouth on 12 March, while Norwich host Manchester City at lunchtime on the same day.
- 22RangelBooked at 90mins
- 3TaylorBooked at 34mins
- 7BrittonSubstituted forFerat 55'minutes
- 10A AyewSubstituted forGomisat 82'minutes
- 23G Sigurdsson
- 9PaloschiSubstituted forBarrowat 45'minutes
- 5MartinBooked at 50mins
- 12BradyBooked at 17minsSubstituted forBennettat 27'minutesBooked at 46mins
- 28O'NeilBooked at 57mins
- 7NaismithSubstituted forBamfordat 64'minutes
- 10JeromeBooked at 13minsSubstituted forMbokaniat 64'minutes
- Craig Pawson
- Shots on Target
Second Half ends, Swansea City 1, Norwich City 0.
Angel Rangel (Swansea City) is shown the yellow card for a bad foul.
Foul by Angel Rangel (Swansea City).
Wes Hoolahan (Norwich City) wins a free kick in the defensive half.
Wayne Routledge (Swansea City) wins a free kick in the attacking half.
Foul by Ivo Pinto (Norwich City).
Foul by Bafétimbi Gomis (Swansea City).
Timm Klose (Norwich City) wins a free kick in the defensive half.
Attempt missed. Patrick Bamford (Norwich City) header from the centre of the box misses to the left. Assisted by Wes Hoolahan with a cross.
Attempt saved. Patrick Bamford (Norwich City) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by Wes Hoolahan.
Foul by Federico Fernández (Swansea City).
Dieumerci Mbokani (Norwich City) wins a free kick on the left wing.
Attempt missed. Nathan Redmond (Norwich City) right footed shot from the centre of the box is close, but misses to the left.
Attempt blocked. Nathan Redmond (Norwich City) right footed shot from the centre of the box is blocked. Assisted by Wes Hoolahan.
Attempt blocked. Patrick Bamford (Norwich City) header from the centre of the box is blocked. Assisted by Nathan Redmond with a cross.
Corner, Swansea City. Conceded by John Ruddy.
Attempt saved. Gylfi Sigurdsson (Swansea City) right footed shot from outside the box is saved in the top left corner.
Bafétimbi Gomis (Swansea City) wins a free kick in the attacking half.
Foul by Ryan Bennett (Norwich City).