Chris Hughton's side raced into a three-goal lead in the first half, before the Swans almost got back on level terms, but managed to hold on for their first away win of the season
Norwich City continued their incredible run of form with an impressive 4-2 win over Swansea City at the Liberty Stadium.
The Canaries raced into a three goal-lead at half-time but allowed the hosts to peg them back to 3-2 in the second half and Michael Laudrup's side pushed for the equaliser before Robert Snodgrass and Michu struck late on but the Canaries hung for the win.
Laudrup made two changes from the win at the Emirates, Danny Graham and Wayne Routledge both returned from injury, with Itay Schechter dropping to the bench and Leon Britton absent altogether. Chris Hughton brought Jonny Howson and Russell Martin back into his starting line-up, as Alexander Tettey and Ryan Bennett made way.
The Swans began the game on the front foot but it was Norwich who had the first chance when Robert Snodgrass' corner was flicked towards goal by Bradley Johnson, but Gerhard Tremmel reacted well in goal.
Swansea continued to enjoy more possession but it was the Canaries, again, who came closest to scoring. Jonny Howson was unlucky to see his superbly struck shot from distance come back off the post.
Hughton's side eventually made the breakthrough after 16 minutes when Steven Whittaker made an excellent surging run forward before playing a one-two with Snodgrass and firing a powerful low shot into the near post.
Swansea's best chance of the half came just before the 30-minute mark, when Graham headed Jonathon De Guzman's cross on to the bar. The hosts’ superior possession wasn’t being counted and they allowed the Canaries to double their lead in the 40th minute.
Snodgrass' free kick was cleared only as far as Holt, who whipped in a cross for Sebastien Bassong to tower of Davies and head into the near corner past Tremmel, who should have done better.
Yet another set-piece delivery from Snodgrass was met this time by the unmarked Grant Holt as the away side went in at the break with a commanding lead through a bullet header into across goal.
And it should have been four for Norwich minutes after the restart; Snodgrass lifted a ball over the Swansea defence for Bradley Johnson who almost scored a sublime goal with an exquisite volley but saw his effort hit the crossbar.
Swansea survived the scare and went straight back up the pitch to pull one back through Michu. The Spaniard swept home Davies' deflected cross into the far corner past Mark Bunn.
Ten minutes later and the comeback was well and truly on. Dyer hooked in a cross which Routledge kept alive. The ball eventually dropped to De Guzman and, 10 yards out, the midfielder fired emphatically past the keeper.
At 3-2, all the pressure was coming from Swansea and the equaliser seemed inevitable but Snodgrass, once again, punished the hosts from a set piece. The former Leeds winger took to goal directly this time, swerving his effort over the wall and into the bottom corner.
Michu made it interesting late one when he turned in a De Guzman's cross in injury-time, but it proved to be too little too late.