Angel Rangel popped up in injury-time to rescue a point for the Swans at Doncaster.
The right-back took down Kemy Agustien's sweet pass, turned his man on the edge of the box and fired an unstoppable strike past Neil Sullivan.
James Hayter had put the hosts ahead early on but the Swans did have chances throughout to level.
Two excellent Dorus de Vries saves from John Oster and David Healy effort kept the score at 1-0 before the late drama at the Keepmoat Stadium.
The Swans made three changes for the game against Doncaster.
There were two forced changes at the back where Neil Taylor and Albert Serran came in, while Ashley Williams was handed the captain's armband in the absence of Garry Monk (injured) and Alan Tate (suspended).
The only other alteration came out wide where top-scorer Scott Sinclair dropped to the bench in place of David Cotterill.
Doncaster:Neil Sullivan, James O'Connor, Mustapha Dumbuya, Wayne Thomas, Sam Hird, John Oster (Dean Shiels, 89'), Brian Stock (C), Mark Wilson, James Coppinger, James Hayter, David Healy (Steve Brooker, 84').
Not Used: Gary Woods (GK), Billy Sharp, Dennis Souza, Adam Lockwood, Waide Fairhurst.
Swans:Dorus de Vries; Angel Rangel, Ashley Williams(C), Albert Serran (Kemy Agustien, 62'), Neil Taylor, Joe Allen, Mark Gower (Stephen Dobbie, 70'), Darren Pratley, Nathan Dyer (Scott Sinclair, 46'), David Cotterill, Craig Beattie.
Not Used:Yves Makabu-Makalambay (GK), Jazz Richards, Cedric van der Gun, Andrea Orlandi.
Attendance: 13,614 Away: 687
Referee: D Deadman (Cambridgeshire)
The people of Doncaster turned out in their numbers and braved the freezing conditions to take advantage of the cut prices on offer to watch their side against the Swans.
And in fairness there were very few red seats on show as they turned up to watch two of the best footballing sides in the Championship.
Rovers boss Sean O'Driscoll was full of praise for his opponents in the pre-match build-up and with barely two minutes played they created their first opening - David Cotterill sneaking in behind James O'Connor to latch on to Mark Gower's pass, Nathan Dyer was ideally placed but the cross was collected by Neil Sullivan.
Donny thought they drew first blood three minutes later when David Healy had the ball in the net, but that was chalked off for offside, while old pro Sullivan was well beaten by Darren Pratley within 60 seconds as Craig Beattie created an opening only for the shot to drop the wrong side of the post.
It was an effort Pratley felt he could have done better and as the game hit the quarter hour mark it was something that went against them as Donny found an effort that did count, John Oster's cross met by the head of James Hayter who found the bottom corner.
It wasn't time to panic and the Swans remained patient in a bid to get themselves back into this game. Cotterill and Neil Taylor were causing problems down the left but it was a Pratley cross that was almost turned into his own net by O'Connor which almost brought the visitors level before the half-hour.
They continued to press and after Gower saw a shot deflect wide his corner was half cleared to Dyer, his effort went straight into the ground and Ashley Williams came to within inches of levelling with an acrobatic strike which dipped wide.
Swansea finished strongly and saw more of the ball but just couldn't force any chances.
Half-Time: Doncaster 1 Swans 0
Scott Sinclair was thrown on in place of Dyer at the break to bring more pace and an added goal threat to the side but the 12-goal wide man endured a disappointing first few minutes as nothing paid off.
The Swans had to wait 10 minutes before creating anything of note when they were awarded a free-kick - Craig Beattie was grounded by Sam Hird - but David Cotterill failed to hit the target from 25-yards out.
And Doncaster could easily have found themselves two-up moments later had it not been for Dorus de Vries who made a fine reflex save to deny former Wales international John Oster, while the follow-up was headed wide by David Healy.
Pratley won his side a free-kick right on the edge of the area which Beattie fired straight at the wall, and from the second attack Pratley had the visitors' best chance as he was played through one-on-one but, as he pulled the trigger, Hird stuck his boot in to deflect the ball over the bar.
A frantic end-to-end spell saw de Vries make another important stop to deny Healy with a header while the Northern Irishman also saw another effort go wide 14 minutes from the end.
But as time ticked down, no matter how hard they tried, breaching the Donny defence was proving to be a difficult task.
Pressure kept being placed on Neil Sullivan's goalmouth and as the game entered four minutes of injury-time the Swans were handed a lifeline.
Substitute Kemy Agustien played a sweet pass into the box where Angel Rangel took the ball down, turned his man and fired an unstoppable strike past the 'keeper and into the net.