The Swans started the new year on a losing note after going down 2-1 at Manchester United.
After a goalless first half, it took United just two minutes after the restart to break the deadlock though Anthony Martial's header.
But the Swans found themselves back on level terms with 20 minutes to go after Gylfi Sigurdsson headed home sub Modou Barrow's fine cross - minutes after Andre Ayew had struck the post.
United, though, were not to be denied and it took some brilliance from Wayne Rooney to seal victory for the hosts with 13 minutes remaining.
There was some late, late drama though as keeper Lukasz Fabianski almost headed into the near corner of the net from a Sigurdsson corner in the last action of the game.
This defeat left the Swans two points above third-bottom Newcastle United after 20 games.
The Swans made seven changes to the starting XI.
From the 0-0 draw at Crystal Palace, Federico Fernandez overcame a heel injury to return to defence along with Angel Rangel.
Leon Britton, Ki Sung-Yueng and Gylfi Sigurdsson all returned along with Wayne Routledge, who was fully fit again after missing the stalemate at Selhurst Park, while Andre Ayew led the line.
Missing for the Swans were left-back Franck Tabanou and striker Eder, as the pair continued their recovery from thigh and ankle injuries.
MANCHESTER UNITED: David de Gea, Phil Jones (Matteo Darmian, ht), Juan Mata, Anthony Martial, Wayne Rooney (capt), Chris Smalling, Daley Blind, Ashley Young (Paddy McNair, 78), Ander Herrera (Michael Carrick, 90), Morgan Schneiderlin, Bastien Schweinsteiger.
SUBS: Sergio Romero, Memphis Depay, Marouane Fellaini, Andreas Pereira.
SWANS: Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Leon Britton (Modou Barrow, 60), Jack Cork, Ki Sung-Yueng, Gylfi Sigurdsson, Wayne Routledge (Jefferson Montero, 82), Andre Ayew (Bafe Gomis, 82).
SUBS: Kristoffer Nordfeldt, Kyle Naughton, Jordi Amat, Matt Grimes.
It proved a tight opening period at Old Trafford, with no real action inside the opening 20 minutes.
Gylfi Sigurdsson's inviting free-kick dropped into the Manchester United box, but no team-mates managed to get onto the end of it.
At the other end, Wayne Rooney drilled his effort into the sidenetting after Ashley Young's cross founds its way to him on the left side of the box.
Wayne Routledge fired a volley straight at David de Gea before the Swans felt they had a strong appeal for a penalty after Morgan Schneiderlin's volleyed clearance struck his hand.
Then the hosts went close to breaking the deadlock as Rooney rose to head Young's cross into the box, but Jack Cork made a vital block and Lukasz Fabianski collected.
As the break approached, Fabianski again did well to deny Juan Mata after the Spaniard drove low when he was found in the box by Young.
Rooney and Young again linked up in the final seconds, with the former rising to meet a cross which Fabianski again comfortably collected.
That proved the final action with the Swans going into the interval pleased with their first half performance.
HALF-TIME: Manchester United 0-0 Swans
United, who made a change at the break as Matteo Darmian replaced Phil Jones, were quick out of the blocks and broke the deadlock within two minutes.
After Rooney's effort was deflected wide for a corner by Ashley Williams, a Young cross found Anthony Martial and he headed past Fabianski from close range.
United continued to push on, but the Swans did well to contain them as they went in search of a second goal.
But, at the other end, the Swans went close to levelling when Andre Ayew rose highest to meet Sigurdsson's cross. While de Gea was left stranded, the ball cannoned back off the post and out of danger.
Soon after, another penalty appeal was waved away when Angel Rangel went down in the box during an attack down the right.
But the visitors did find the outcome they were looking for with 20 minutes to go.
When Rangel touched right to Barrow, the Gambian's perfect cross found Sigurdsson, who deftly headed into the far corner.
United, though, were not to be on level terms for long as Martial's powerful low cross was superbly flicked home by Rooney just seven minutes later.
The Swans needed a response quickly, and Barrow's pace was evidently causing the home defence problems.
And it was the winger who went close for the Swans as he cut inside before firing a low shot at de Gea.
The Swans then made a double change for the last eight minutes as Jefferson Montero and Bafe Gomis replaced Routledge and Ayew.
In stoppage time, skipper Williams was denied from 20 yards as de Gea reacted well to pad his stinging drive for a corner.
And the drama continued until the very last second as, from a Swans corner, Fabianski went up and rose highest but he could only head inches wide of the near post.