Oxford United caused an FA Cup upset as the League Two side dumped the Swans out at the third-round stage.
The Premier League visitors went ahead after Jefferson Montero finished superbly following a neat run which saw him latch onto Marvin Emnes' return pass before slotting home after 23 minutes.
But the hosts were level as Liam Sercombe converted his spotkick just before the break to set up a tense second half.
Oxford were quick out of the blocks and Kemar Roofe rifled home from an angle to send the hosts ahead, before he added a second just before the hour mark.
Bafe Gomis started the Swans' revival by stroking home the visitors' second with 66 minutes on the clock.
The French striker was then denied a dramatic equaliser with five minutes left, with a timely block diverting his effort out for a corner.
But that was the end of the action as the Swans' FA Cup adventure ended at the first hurdle.
The Swans handed a debut to youngster Liam Shephard as Alan Curtis made ten changes for the FA Cup tie at Oxford United.
Pentre-product Shephard - Yeovil's young player of the year in 2014-15 following a four-month loan spell - made his first Swans appearance at right-back, having appeared as a substitute on six occasions last season.
Jack Cork was the only one to remain in the starting XI from the Premier League defeat at Manchester United as Alan Curtis, who was confirmed as manager for the remainder of the season in midweek, gave valuable game-time to his squad.
Swedish international Kristoffer Nordfeldt started in goal while Jordi Amat, Kyle Bartley and Franck Tabanou, who had recovered from a thigh problem to make his first appearance since the Capital One Cup loss at Hull City in September, joined Shephard in defence.
Matt Grimes linked up with England international Jonjo Shelvey and Cork in midfield, while Marvin Emnes and speedster Jefferson Montero provided the width, with French striker Bafe Gomis leading the line.
On the bench, 18-year-olds Joe Rodon and Daniel James were included in the matchday squad for the first time along with Stephen Kingsley, while Eder had fully recovered from an ankle injury.
OXFORD UNITED: Sam Slocombe, George Baldock, Joe Skarz, Kemar Roofe (Pat Hoban, 90), Johnny Mullins, Jake Wright (capt), Liam Sercombe, Alex MacDonald (Callum O'Dowda, 71), John Lundstram, Ryan Taylor (Danny Hylton, 79), Chris Maguire.
SUBS: Benji Buchel, Josh Ruffels, Cheyenne Dunkley, Jordan Evans.
SWANS: Kristoffer Nordfeldt, Liam Shephard, Jordi Amat, Kyle Bartley (capt), Franck Tabanou (Stephen Kingsley, 60), Jack Cork, Matt Grimes (Modou Barrow, 75), Jonjo Shelvey, Marvin Emnes, Jefferson Montero, Bafe Gomis.
SUBS: Gerhard Tremmel, Joe Rodon, Jay Fulton, Daniel James, Eder.
The Swans started brightly in the opening exchanges, with Jefferson Montero wasting a great opportunity to take an early lead as he skied Marvin Emnes' cross from close range.
Jonjo Shelvey then showed his intentions with two long-range efforts after working himself into space, but he failed to find the target.
Oxford also caused concern around the 20-minute mark as Kemar Roofe rose highest to meet a cross, but his headed effort dropped onto the top netting.
Then Kristoffer Nordfeldt was called into action for the first time as he had to react quickly to tip Ryan Taylor's header over a corner.
At the other end, Emnes was denied by a timely block before the Swans broke the deadlock with 23 minutes on the clock.
It started with a fine run down the left by Montero, and when he latched onto Emnes' perfect return pass inside the box, the Ecuadorian winger tapped home past keeper Sam Slocombe.
Oxford went in search of an equaliser, and Chris Maguire was denied by Nordfeldt while John Lundstram blazed over from 20 yards.
It was entertaining stuff, and the Swans were keen to find another goal to give themselves breathing space.
And Shelvey went close to doing that as, after he volleyed wide, the England midfielder curled a free-kick around the wall and into the sidenetting.
But, in a frantic finale to the half, Oxford got themselves back onto level terms from the penalty spot.
After Jake Wright saw his effort expertly saved by Nordfeldt, Kyle Bartley was adjudged to have brought down an Oxford player in the box. And Liam Sercombe blasted straight past the Swedish keeper to send the teams into the break on level terms.
HALF-TIME: Oxford United 1 Swans 1
Oxford started the second half just as they ended the first, with the hosts taking a shock lead.
Just three minutes after the restart, Roofe drilled a powerful effort from the left-hand side of the box into the bottom right corner.
The Kassam Stadium erupted as the home fans sensed an upset was on the cards.
And they were on their feet once again as they doubled their lead just before the hour mark.
It came from a Swans corner, which was a result of Slocombe tipping Jack Cork's goalbound header over, as Maguire raced on to counter and feed Roofe, whose effort struck Nordfeldt but bounced over the line.
But the Swans gave themselves hope as they pulled one back after 66 minutes.
Cork was instrumental, collecting Bafe Gomis' pass before his sublime through ball found the unmarked Frenchman, and he slotted home from close range.
It set up a tense finish at the Kassam Stadium, with both teams going in search of the game's sixth goal.
Gomis went close to levelling in the final five minutes as sub Modou Barrow found him in the box, but the striker was denied by a fine block was diverted his effort for a corner.
But that was the end of the action as the Swans were among the Premier League scalps to fall at the first hurdle.