The Swans suffered only a second home league defeat of the season as they were on the wrong end of a seven-goal thriller with Norwich City.
Michael Laudrup’s side found themselves 3-0 down at the break after Steven Whittaker, Sebastian Bassong and Grant Holt found the net.
After the break, a resurgent home side made a brave comeback as Michu streered home Ben Davies’ cross before Jonathan de Guzman volleyed home another.
Sub Itay Shechter then fired home only for his strike to be ruled out for a foul on keeper Mark Bunn by Michu, before Robert Snodgrass curled home a free-kick to make it 4-2.
Michu then headed home de Guzman's cross in stoppage time for his 12th league goal of the season, but the points went to the visitors.
It means Norwich continued their good form against the Swans, having won the last three meetings between the sides.
The Swans made two changes from the side that won at Arsenal.
Leon Britton was ruled out through a knee injury picked up in training, which meant a midfield trio of Ki Sung-Yueng, Jonathan de Guzman and Michu. Wayne Routledge returned on the wing after missing out at Arsenal while Danny Graham recovered from illness to make his first appearance since the win at Newcastle. Graham, who scored twice in the home defeat to Norwich last season, started up front in place of Itay Shechter, who dropped to the bench.
Swans: Gerhard Tremmel, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Ki Sung-Yueng, Jonathan de Guzman, Michu, Nathan Dyer, Wayne Routledge, Danny Graham (Itay Shechter, 69).
Subs: David Cornell, Dwight Tiendalli, Kyle Bartley, Garry Monk, Kemy Agustien, Luke Moore.
Norwich: Mark Bunn, Russell Martin, Steven Whittaker (Leon Barnett, 90), Bradley Johnson, Sebastien Bassong, Robert Snodgrass, Jonathan Howson, Grant Holt (capt, Steve Morison, 83), Anthony Pilkington, Wes Hoolahan, Javier Garrido.
Subs: Declan Rudd, Simeon Jackson, David Fox, Elliott Bennett, Marc Tierney
The Canaries got off to a flying start, Bradley Johnson getting onto the end of Robert Snodgass' corner inside the first minute and it took a great reflex save from Gerhard Tremmel to keep the header out.
Danny Graham then beat Sebastian Bassong to Angel Rangel's cross but that dropped wide as the Swans made an instant reply to the visitors' early threat.
Graham again threatened after he was teed up by Ben Davies' tap down from a Jonathan de Guzman crossfield cross, but the striker couldn't find the target.
The visitors then went within inches of opening the scoring, Jonathan Howson's shot striking the post and Jonathan Howson's effort just being collected by Tremmel.
But Norwich did get their goal on 16 minutes, ex-Rangers full-back Steven Whittaker took play into the box before cutting inside on his left foot before firing into the bottom corner past Tremmel.
The Swans needed a response, and they went within inches of levelling after 28 minutes as Graham beat Whittaker to de Guzman's cross, but Graham's looped over Mark Bunn and smashed off the crossbar.
Michu then glanced his header wide from Angel Rangel's cross as the hosts upped the pressure in pursuit of an equaliser.
The Spaniard then saw his effort deflect off Wayne Routledge and spin just wide of the far corner before the visitors doubled their lead.
Holt's cross to the back post found Bassong, who leapt above Ben Davies and squeezed his header in at the back post despite Tremmel getting a hand to it.
It got worse for the hosts, with provider Holt turning scorer in the 44th minute. Snodgrass' free-kick was inch perfect for the striker, who powerfully headed past Tremmel and into the corner.
Half-time: Swans 0 Norwich 3
The Swans needed an early goal if they were to get back into this contest, but it was the visitors who almost grabbed the next goal within two minutes of the restart.
Bradley Johnson latched onto a through ball and beat the offside trap, but his shot thundered off the crossbar.
But with 51 minutes on the clock, the Swans did pull one back.
Ben Davies’ low cross found Michu, who directed his effort past Mark Bunn from 12 yards.
The Swans came again, Michu sliding through a pass for Graham, but his left-footed shot on the turn was dealt with by Bunn.
The Swans kept plugging away, and in the 59th minute they got another goal. Rangel sent a sublime ball down the right flank for Dyer to race on to. His cross was nodded out only to de Guzman, who volleyed into the bottom corner.
The Liberty almost erupted once again eight minutes later as Routledge’s chipped pass sent Graham in on goal, but the Norwich defence got back in time to cover.
It was Graham’s last involvement, with Itay Shechter replacing him on 69 minutes.
The Swans had the ball in the net a third time, as Bunn spilled under pressure from Michu and Shechter fired in, but referee Howard Webb ruled it out for a foul on the keeper.
Unbelievably, the sixth goal of the game arrived.
It went to the visitors, with Snodgrass curling an unstoppable free-kick home from 20 yards into the near corner after a Williams foul on Holt.
With the Swans looking for a reply Dyer slid through a pass for Michu, who stretched out and fired just wide as the clock ticked towards the final five minutes.
Chico Flores went close in the dying stages, and then when Michu headed home from Jonathan de Guzman's cross in stoppage time, it set up a tense finish.
But the points went to Norwich, who held on in a thrilling Premier League encounter.