The Swans went down 3-0 at Manchester City after goals in each half from Alvaro Negredo and Samir Nasri.
Negredo opened the scoring after eight minutes with a sublime free-kick which nestled into the corner from 20 yards before French midfielder Nasri fired in from close range just before the hour.
His second - and City's third - came in the 77th minute as he finished off the Swans' hopes with a neat finish from a Pablo Zabaleta cross.
The Swans, though, had enjoyed the better share of possession and chances after the opening goal and they should have gone into the break on level terms.
Jonjo Shelvey was a constant menace to the hosts, and he was twice denied by fine stops from keeper Costel Pantilimon.
The best chance of the first half for the Swans fell to Jonathan de Guzman, who nutmegged Martin Demichelis but he could only fire his shot over the crossbar.
But City were clinical, and they rose to third after this victory while the Swans dropped to 13th in the table.
The Swans made seven changes to the starting XI.
Three of them came in defence as Dwight Tendalli started at right-back due to Angel Rangel's injury picked up in the Europa League defeat to Valencia in midweek.
Ashley Williams returned to captain the side while fellow Wales international Ben Davies got the nod at left-back.
Spaniard Jose Canas was back in midfield in place of the injured Leon Britton, who had a toe problem, while Pablo Hernandez made his first start since the 2-0 win over West Brom on September 1.
Up front, Alvaro Vazquez led the line as record signing Wilfried Bony was ruled out with a hamstring injury.
Manchester City made just one change to their starting line-up as Joleon Lescott replaced Matija Nsatasic, who was missing through injury.
MAN CITY: Costel Pantilimon, Pablo Zabaleta, Joleon Lescott, Martin Demichelis, Gael Clichy, Fernandinho, Yaya Toure (capt), Jesus Navas (Aleksandar Kolarov, 76), Samir Nasri, Alvaro Negredo (James Milner, 62), Sergio Aguero (Edin Dzeko, 79).
SUBS:Joe Hart, Micah Richards, Javi Garcia, Jack Rodwell.
SWANS: Gerhard Tremmel, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Jose Canas, Jonathan de Guzman, Jonjo Shelvey, Alejandro Pozuelo (Nathan Dyer, 67), Pablo Hernandez (Wayne Routledge, 62), Alvaro Vazquez.
SUBS: Michel Vorm, Jordi Amat, Neil Taylor, Roland Lamah, Rory Donnelly.
The hosts made a strong start, and after some early probes they took the lead.
After seeing Sergio Aguero test Gerhard Tremmel after just 30 seconds, Alvaro Negredo gave Manchester City the lead with eight minutes on the clock.
Following a foul on Negredo by Jose Canas, the striker picked himself up to curl home past Tremmel with a sublime free-kick.
The Swans went in search of an instant response and Jonjo Shelvey went close to equalising but his curling right-footed effort was tipped wide by Costel Pantilimon for a corner.
Shelvey tested the keeper again, his powerful low effort drawing some quick reflexes out of Pantilimon as he dived down to again tip it wide for another corner.
The midfielder was finding himself in space, particularly on the counter attack, and when Shelvey threaded through a pass through the legs of Joleon Lescott to Alvaro Vazquez, the Spaniard had a decent opportunity but his shot on the turn was scuffed wide.
At the other end, Tremmel had to be on his toes to deny Aguero from close range following Gael Clichy's pass. And, from the resulting corner, Martin Demichelis rose highest but saw his header cannon back off the crossbar before Aguero nodded wide from the loose ball.
The Swans then felt they had a good shout for a penalty after Pablo Hernandez went down under a challenge by Demichelis, but referee Mark Clattenburg turned down the appeals.
Then the visitors created a golden opportunity as Jonathan de Guzman nutmegged Demichelis following Shelvey's inside pass, but when the Dutchman closed in on goal, he fired over from 18 yards.
Michael Laudrup's side were enjoying a good share of possession and chances, and they will have taken heart from their response to going a goal behind early on as they headed down the tunnel at half-time.
HALF-TIME: Man City 1 Swans 0
Both sides created early chances after the restart, with Tremmel clearing an Ashley Williams pass-back after he slid in to dispossess Negredo as he was about to pull the trigger while Aguero fired into the sidenetting after controlling a Yaya Toure pass before riding Williams' challenge and rounding Tremmel.
The Swans kept plugging away too, and de Guzman again outpaced Demichelis in the box before Pantilimon kept out his effort from an angle.
But, with 58 minutes on the clock, Manchester City doubled their advantage.
Yaya Toure raced on and found Samir Nasri racing into the box, and he controlled perfectly before evading the sliding challenge of Williams before cutting his shot back across goal and into the bottom corner.
Laudrup's side went in search of cutting the deficit and when Hernandez was teed up by Pozuelo following a surging run by Shelvey, the Spaniard couldn't keep his effort down from 12 yards out.
It proved the winger's final involvement as he was replaced by Wayne Routledge just past the hour.
The action continued at both ends, and Pablo Zabaleta chipped over before Aguero sliced his volley over after a melee in the box, and, soon after, then the striker saw his angled drive bounce wide.
Then the third arrived. With 77 minutes on the clock, Zabaleta's cross found Nasri and he turned his shot into the corner of the net.
Nasri went within inches of claiming a hat-trick with minutes remaining as his curling effort just past the post after he was set up by sub Edin Dzeko.
And, late on, de Guzman headed over from a Ben Davies cross in what proved the final action of the game.