SWANSEA 3 CITY 4
Goals from Steven Whittaker, Sebastien Bassong and Grant Holt had given the visitors a 3-0 lead at the break, but Swansea took control of the opening 20 minutes of the second half to pull back two goals through Michu and Jonathan de Guzman.
A Robert Snodgrass free kick then put City 4-2 ahead before Michu’s late strike set up a nervy finish, but Chris Hughton’s side saw out the win – their ninth Premier League game without defeat.
Hughton made two changes from the win over Sunderland last weekend - Ryan Bennett and Alex Tettey were missing from the final 18 - with Russell Martin and Jonny Howson returning to the starting eleven in their place. Martin slotted in at centre-back for the first time this season with Steven Whittaker staying at right-back. Howson partnered his former Leed's team-mate Bradley Johnson in central midfield.
The Swans welcomed back striker Danny Graham who had a productive goal scoring record against the Canaries going into this game - scoring six times in the four games he featured in for both Swansea and Watford against City.
The Canaries won a corner through Robert Snodgrass in the opening minute - the Scot taking the set-piece and Johnson getting a touch to send it goalwards only for Gerhard Tremmel to get a hand to deny the City midfielder.
It was a bright start from the visitors and five minutes later Johnson almost put Holt through on goal but his pass was a little too strong.
Swansea's first real opportunity came on 10 minutes when Danny Graham turned on the edge of the box and shot, but it was high and wide of Mark Bunn's goal.
On 14 minutes the Canaries went close to taking the lead with two good opportunities - they had worked the ball well around the Swan's half and the ball fell to Howson who faked a pass out to Snodgrass then stepped forward and hit a shot which went across goal and hit the post - it was then worked back out again and under pressure from Holt Tremmel punched it out to Snodgrass who attempted to lob the Swansea 'keeper but he got his hands on the ball to collect.
But two minutes later City were ahead - a one-two between Whittaker and Snodgrass deep in the Swansea half then saw the defender go on a bursting run past one defender to the edge of the area, turned and hit a powerful left-footed shot past Tremmel. A great solo effort and the Scot's first goal for the Club since his summer move from Rangers.
On 20 minutes referee Howard Webb awarded the hosts a free kick 22 yards from City's goal, but Jonathan de Guzman's effort didn't get beyond the Canary wall and City broke themselves.
Snodgrass went close to doubling the lead after 26 minutes when he pushed down the left and cut inside into the area, but the sting was just taken out of his shot as it hit left-back Ben Davis and although Tremmel was wrong footed he had time to step across and pluck the goalwards ball out of the air.
This was swiftly followed by Swansea's best effort so far when de Guzman swung in a cross for Graham - who rose well and nodded a well-placed header over Bunn but thankfully it clipped the bar and bounced away to safety.
It gave the Swans some renewed confidence and Angel Rangel's right-wing cross found top-scorer Michu with a diving header but the Spaniard was wide of the far post.
The Canaries were starting to live dangerously another cross from the right luckily going behind Dyer and Michu and away and then on 34 minutes the Spaniard had a deflected shot which just dribbled past the far post with Bunn wrong-footed.
However, with five minutes of the half left City gave themselves a two-goal lead when Holt sent in a great cross to the back post where Bassong, still forward from a free-kick moments earlier, was waiting and squeezed in a header past Tremmel for his third goal in four games.
And the travelling Yellow Army were sent in to raptures just two minutes later when the City skipper made it 3-0. Snodgrass won another free-kick far right and sent in a beautiful delivery right on to Holt's forehead and he buried his header into the bottom corner.
On the stroke of half-time Swansea were awarded a free-kick when Martin fouled Michu - the City defender picking up the first yellow card of the game. Ki Sung-Yueng stepped up but although his effort was on target it was straight into the grateful arms of Mark Bunn.
HALF-TIME: Swansea City 0, Norwich City 3
There were no changes for either side at half-time. Swansea opened the half by winning a corner in the first minute but it was a disappointing delivery by de Guzman and city cleared the danger.
Bradley Johnson went very close to extending City's lead when he took control of a Snodgrass chip into the area and hit a shot against the underside of the bar.
But six minutes into the half it was Swansea who struck home - Davies' ball from the left went across the penalty area and Michu was on hand to slot it home to give the hosts hope.
With the home crowd buoyed by the goal Swansea were pushing forward and Michu tried to turn provider on 56 minutes when he found Graham in a good position, but Bunn was on hand to make a good stop from the former Hornet.
But unfortunately just before the hour Swansea did pull back another goal through Jonathan de Guzman when he struck well inside the area, filling the Swans with great confidence which the Canaries just didn't want with half an hour to play.
City were now having to dig deep as Swansea were keeping the ball well - although on the break the Canaries were finding space. Pilkington on 67 minutes running down the left and putting in a ball for Holt, but he was well marked by Ashley Williams.
Javier Garrido made a good challenge to deny Graham space and give Bunn time to claim the ball as the Swans' striker looked to pounce. it was to be his last contribution as he was replaced by Itay Shecter on 69 minutes.
And two minutes after coming on Shecter thought he'd put Swansea level when he turned in a high ball under pressure from Bunn, but referee Howard Webb awarded a foul on the City stopper and disallowed the goal to the relief of the Canaries.
With 15 minutes of the half left Grant Holt was put through by Wes Hoolahan only to be taken down by Williams - the Swansea skipper receiving a yellow card after not being deemed the last defender.
And from the free-kick a little of the pressure was relieved when Snodgrass stepped up to curl his effort delightfully past Tremmel for 4-2. What a game this was proving to be.
With seven minutes left came City's first substitution which saw Steve Morison replace Holt up front.
Although City's fourth goal had subdued Swansea a little there was no doubting the quality of their leading scorer and he nearly converted again when Dyer put in a neat ball for him to turn and swivel, just pulling his shot wide.
With three minutes left to play Chico Flores had a drive from distance which sailed just over the bar.
Three minutes of additional time were added, which saw Garrido make another good interception at the feet of Dyer to concede a corner. From the resulting flag-kick the ball was worked out and de Guzman put the ball back in for Michu to head the ball over the line for 4-3 and a grandstand finish.
But thankfully the final whistle went to bring to an end a very entertaining game and City's first away win of the season.
FULL-TIME: Swansea City 3, Norwich City 4
SWANSEA: Tremmel, Flores, Williams (c), Michu, Graham (Shecter 69), Dyer, Routledge, de Guzman, Rangel, Sung-Yueng, Davies. Subs not used: Cornell, Bartley, Monk, Moore, Tiendalli, Agustein.