The New Year got off to a losing start for the Swans as they went down 3-2 at home to title-chasing Manchester City.
Michael Laudrup's side had found themselves behind after 14 minutes via Fernandinho's shot which found its way to the net through a crowded box.
But the Swans were level at the break as Wilfried Bony - who had earlier struck the post - headed home Jonathan de Guzman's cross in added-on time.
It had been a promising first half for the hosts, but Manuel Pellegrini's side would go on to claim victory with two goals in nine minutes after the break.
Firstly, Yaya Toure's effort found the net after deflecting off Ashley Williams in the 57th minute, and then Aleksandar Kolarov raced on from the halfway line before his rasping shot beat Gerhard Tremmel, despite the German keeper getting a slight touch.
Bony then pulled one back in the 90th minute - his 12th of the season - as he fired home a thunderous shot into the bottom corner from 25 yards.
But it wasn't enough as the visitors held out through the three minutes of added-on time.
Defeat was a disappointing start to 2014 for the Swans, which was made worse by an injury to Spanish international Pablo Hernandez after just ten minutes.
The Swans made two changes to their starting XI.
Angel Rangel started at right-back in place of Dwight Tiendalli while Wayne Routledge was given the nod on the wing as Roland Lamah - scorer of the Swans' goal in the 1-1 draw at Aston Villa - dropped to the bench.
Michael Laudrup was without Leon Britton, who missed out through illness, while Michel Vorm, Nathan Dyer and Michu were still sidelined.
Joe Hart was available for the visitors despite requiring five stitches in a gash under his left eye while David Silva was suspended.
Sergio Aguero, Martin Demichelis, Stevan Jovetic and Micah Richards remained injured for Manchester City.
SWANS:Gerhard Tremmel, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Jose Canas, Jonathan de Guzman, Jonjo Shelvey (Alejandro Pozuelo, 81), Wayne Routledge, Pablo Hernandez (Roland Lamah, 10), Wilfried Bony.
SUBS: Gregor Zabret, Dwight Tiendalli, Jordi Amat, Neil Taylor, Alvaro Vazquez.
MANCHESTER CITY:Joe Hart, Pablo Zabaleta, Vincent Kompany (capt), Matija Nastasic, Aleksandar Kolarov, Jesus Navas (Jack Rodwell, 90), Fernandinho, Yaya Toure, Samir Nasri (James Milner, 70), Alvaro Negredo (Javi Garcia, 59), Edin Dzeko.
SUBS: Costel Pantilimon, Joleon Lescott, Gael Clichy, Dedryck Boyata.
In a busy start to the match, Edin Dzeko fired wide from Alvaro Negredo's low cross while Wilfried Bony struck the post from 25 yards with a powerful effort.
The Swans were forced into a change after ten minutes as Pablo Hernandez pulled up with what appeared to be a hamstring injury, and he was replaced by Roland Lamah.
But, just four minutes later, the Swans found themselves behind as Fernandinho thundered a low shot through a crowded area after a corner had deflected to him off the body of Jonathan de Guzman.
The Swans went in search of an equaliser, and Jonjo Shelvey created space for himself 20 yards out but he sliced his shot wide as the visiting defence closed in.
They created another chance with a fine passing move started by de Guzman inside his own half, and when Bony and Lamah linked up to send the Dutchman in on goal, he failed to make a proper connection with Joe Hart comfortably saving.
Moments later de Guzman saw his free-kick bounce off the wall and straight to Jose Canas, but he failed to trouble Hart as his half volley skimmed wide.
City responded with a Dzeko shot that deflected off Chico Flores and just past the far post for a corner as Gerhard Tremmel scrambled across goal.
The Swans then felt they had a strong penalty appeal after Ashley Williams' shot struck the arm of Vincent Kompany, but referee Phil Dowd waved away the pleas.
Michael Laudrup's side were pushing and pushing for an equaliser, and they were enjoying a period in which they were starting to dominate.
Another slick passing move saw them go within inches of levelling as Bony linked with Shelvey, and the striker latched onto the latter's pass before his blistering shot across goal bounced just wide of the far post.
But, with three minutes of added on time, the Swans did get back on level terms.
After Wayne Routledge held up play, he touched wide to de Guzman, and his curling cross met Bony, who leapt to direct his header just inside the near post.
HALF-TIME: Swans 1 Manchester City 1
There were few chances in the opening exchanges after the break, with Negredo's weak volley saved comfortably by Tremmel while de Guzman drove his 20-yard free-kick over.
But, with 57 minutes on the clock, the visitors were back in front.
After Tremmel punched Navas' cross to the edge of the box, Yaye Toure held off Jose Canas before his shot deflected off Williams and into the far corner of the net.
It got worse for the Swans as Manuel Pellegrini's side doubled their lead in the 66th minute, with Aleksandar Kolarov winning possession off Routledge inside his own half before the full-back raced on into the Swans box before firing home with Tremmel unable to keep out his thunderous effort.
The Swans were in desperate need of pulling a goal back, and Bony - a nuisance to the City defence all game - drew a save from Hart after he had wrongfooted the visiting defence before unleashing a powerful left-footed drive.
But Bony wouldn't be denied any further, as he thundered home a rasping 25-yard shot in the 90th minute which soared into the bottom corner of the net with Hart helpless.
But the visitors held out further pressure from the Swans, with Pellegirini's side seeing out the three minutes of added on time.