A brace from Jonathan de Guzman fired Swansea to their first win in 10 games and gave them some much-needed breathing space above the relegation scrap.
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The Welsh side had never beaten Norwich in their five Premier League meetings before this match. But two clinical finishes from the Dutchman plus a 75th-minute goal from winger Wayne Routledge banished that bogey at the Liberty Stadium.
A 3-0 victory was the least Garry Monk's side deserved as they dominated both halves and, but for some jittery moments after the break, never looked in trouble.
The first chance fell to Michu in the eighth minute. The Spanish marksman latched onto a pass from Angel Rangel just outside the box but dragged his effort wide.
There were plenty of lateral passes but little penetration from the Swans in the early stages as Norwich stood firm and held their rigid 4-4-2 formation. But as the half wore on the cracks opened up.
Michu again shot wide in the 24th minute and a low save from Canaries goalkeeper John Ruddy, followed by an urgent clearance from midfielder Wes Hoolahan, was needed to repel Routledge during the next attack.
De Guzman bagged a deserved opener on the half-hour. It was midfielder Jonjo Shelvey - involved in most of his side's good work - who delivered the initial cross from the right.
When the visitors' defence failed to clear under pressure from Michu and Routledge, De Guzman was there to pounce and rifled home from 18 yards for his fourth league goal of the season.
Sublime skill from Wilfried Bony laid the second on a plate for De Guzman after 38 minutes. As the midfielder played it into feet there was no clear route to goal. But the Ivorian top scorer showed he can create as well as bang in the goals by performing an audacious drag over and back-heel to return the ball to De Guzman, who finished coolly, off the post.
The Canaries had little to show for their efforts in the first half - a couple of corners and a tame shot from full-back Russell Martin their only signs of promise.
The jitters struck for the Swans straight after the break. Skipper Ashley Williams had to clear a Bradley Johnson shot from the goal line and Michel Vorm struggled to deal with a downward header from Ricky van Wolfswinkel.
Shelvey went close after some great interplay down the left, then he turned provider when he set De Guzman away from inside his half, racing towards goal. His lay-off to Bony was fired over, but reminded the visitors of the perils of committing too many players forward in search of a goal.
With 20 minutes to go the Swans began to open up, threading cute passes and forcing some scrambled defence from the Canaries. Michu made way for Pablo Hernandez to a standing ovation. He is still not back to his best but appears to be improving with every minute of action after his long injury lay-off.
Leon Britton - making his 400th league start for Swansea in a career that has spanned all four divisions - beavered away in midfield all day.
Routledge put the result beyond doubt when he ran behind the defence and calmly finished off a Shelvey through-ball.
Another Bony back-heel led to confusion in the Canaries' defence, causing skipper Sebastien Bassong to strike the ball against his own post.
Chris Hughton's Canaries could not muster any consolation as the clock ticked down to Swansea's fifth home league win in the last 21.
Meanwhile, Norwich's away woes continue, having picked up only two points from the last 24 on the road.