The Swans suffered a second defeat at the hands of Manchester City within three days as Pep Guardiola's side maintained their perfect start to their Premier League campaign.
Sergio Aguero put the visitors ahead within nine minutes, but the Swans were soon back on level terms after Fernando Llorente scored his first goal for the club with a stunning half-volley.
Both sides created chances before the break, but it was the visitors who pushed on in the second half.
The Swans' best chance of taking the lead saw Gylfi Sigurdsson volley wide from Wayne Routledge's cross, but City were to break the deadlock.
It came from the penalty spot after referee Neil Swarbrick adjudged Mike van der Hoorn to have used his elbow in a challenge with Kevin De Bruyne.
Up stepped Aguero, and the striker coolly finished to grab his second of the afternoon.
Raheem Sterling then made it 3-1 after he finished off a superb counter attack by the league leaders, who picked up their sixth consecutive victory.
Defeat left the Swans on four points from six games.
The Swans made four changes to the starting line up.
From the EFL Cup defeat to Pep Guardiola's side, the Swans welcomed back Lukasz Fabianski in goal while Leroy Fer, Gylfi Sigurdsson - who made his 150th Premier League appearance - and Fernando Llorente also started.
Kyle Naughton reverted from right wing to left-back while Mike van der Hoorn made his Premier League debut in the heart of defence.
On the bench, Alfie Mawson made his first appearance in the matchday squad while record signing Borja was also among the substitutes.
Francesco Guidolin was without defender Federico Fernandez, who was ruled out with a groin strain, along with Nathan Dyer, who underwent an ankle operation on Monday.
SWANS: Lukasz Fabianski, Angel Rangel, Jordi Amat, Mike van der Hoorn, Kyle Naughton, Leon Britton (capt, Borja, 79), Jack Cork (Ki Sung-Yueng, 73), Leroy Fer, Gylfi Sigurdsson, Wayne Routledge (Modou Barrow, 73), Fernando Llorente.
SUBS: Kristoffer Nordfeldt, Alfie Mawson, Neil Taylor, Jefferson Montero.
MANCHESTER CITY: Claudio Bravo, Bacary Sagna (Pablo Zabaleta, 78), Raheem Sterling, Ilkay Gundogan (Fernando, 68), Sergio Aguero, Aleksandar Kolarov, Kevin De Bruyne (Jesus Navas, 81), David Silva (capt), John Stones, Fernandinho, Nicolas Otamendi.
SUBS: Willy Caballero, Leroy Sane, Gael Clichy, Kelechi Iheanacho.
The game sprung into action in the early stages, with both teams showing their attacking intent.
Just three minutes were on the clock when Gylfi Sigurdsson's cross found Wayne Routledge at the back post, but Claudio Bravo denied him.
Sigurdsson then had the ball in the net just two minutes later when he fired in a volley, but it didn't count as referee Neil Swarbrick had already blown his whistle.
Manchester City then had the ball in the net themselves after nine minutes, and this time it counted as Bacary Sagna's cross found Sergio Aguero, and the striker's perfect first touch allowed him to turn and fire through the legs of Lukasz Fabianski.
The Swans needed a response, and, after Fernando Llorente was denied from close range, the striker fired the hosts level with a thunderous shot.
The equaliser came four minutes after the Swans fell behind, with Sigurdsson finding Llorente on the edge of the box, and he controlled possession before firing into the far top corner.
The game continued to ebb and flow, and Fabianski had to race off his line to deny the onrushing Raheem Sterling.
Aguero then saw his effot dip onto the top of the net before Kevin De Bruyne - in on goal after latching onto Ilkay Dungongan's through ball - uncharacteristically scuffed wide from 20 yards.
Then, with the game entering added on time, Mike van der Hoorn was quickest to react when a free-kick was nodded back across goal, with the Dutch defender just clearing in time before David Silva pounced.
It was thrilling stuff, with the action proving end to end.
But that was the final action of the first half, with both teams going into the break on level terms.
Half-time: Swans 1 Manchester City 1
The match continued its quick tempo after the break, with Routledge's cross following a one-two with Sigurdsson just evading Llorente.
Then Sigurdsson volleyed wide after Llorente had chested down a high Routledge cross while, at the other end, John Stones headed powerfully wide from a Silva corner.
The Swans had a great chance to take the lead when some fine play by Routledge saw him hold off Aleksandar Kolarov before finding Sigurdsson 15 yards out. But his first-time volley sailed high and wide.
But City were always a massive threat going forward with their pace and movement.
And it took a superbly-timed block from Jordi Amat to deny Agero six yards out.
But, with 65 minutes on the clock, the visitors were back ahead as referee Swarbrick pointed to the penalty spot after ruling Mike van der Hoorn to have used his elbow against De Bruyne.
Up stepped Aguero, and he chipped home to put City 2-1 up.
The Swans made a double change with Ki Sung-Yueng and Modou Barrow replacing Cork and Routledge.
But, in a fine counter attack following a Swans corner, City extended their lead in the 77th minute.
After chaging down Leon Britton's pass, City raced forward and Sterling eventually fired home from close range.
It almost got even worse for the Swans, but Fabianski dived low down at full stretch to stop sub Fernandinho from point-blank range.
That was the end of the action at the Liberty, with the Swans suffering another defeat despite a promising performance.