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Kemar Roofe was Oxford's two-goal hero as Swansea found themselves on the wrong end of the first major upset of the FA Cup third round.
Former West Brom youngster Roofe scored twice in the second half as the League Two Us came from behind to stun the Premier League side 3-2.
Alan Curtis made 10 changes for his first match since being named Swans manager until the end of the season - then watched in horror from the touchline as the decision backfired spectacularly.
There was little sign of the drama to come when Swansea took the lead, albeit against the run of play, thanks to a stylish goal by Jefferson Montero.
Oxford deservedly hit back through Liam Sercombe's penalty before half-time, and then Roofe blew the Swans away with his quickfire double after the break.
Bafetimbi Gomis pulled one back but the visitors could not find an equaliser and slipped to a chastening defeat.
United boss Michael Appleton vowed not to change his side's passing style - despite taking on one of the Premier League's pass masters - and at times it was hard to tell which side was 54 league places above the other.
Certainly Oxford carved out the better chances in the opening half an hour, while Swansea seemed to be relying on the scattergun approach to shooting favoured by Jonjo Shelvey, with predictably dire results.
Roofe headed George Baldock's cross narrowly over before Ryan Taylor's header was only kept out by a fingertip save from Swans keeper Kristoffer Nordfeldt.
Yet just as Oxford were building up a head of steam, the Swans brought a genuine touch of top-flight class to the proceedings.
A swift counter-attack saw Montero charge into the area, play a neat one-two with Marvin Emnes and impudently back-heel the ball past United goalkeeper Sam Slocombe.
But with half-time approaching Oxford were gifted a way back into the game by stand-in Swans skipper Kyle Bartley.
Nordfelt had pulled off a fine save to keep out Jake Wright's shot, but when the rebound eventually fell to Alex McDonald, Bartley inadvisedly slid into the midfielder.
Contact may have been minimal but it was a ridiculous challenge in the area and referee Kevin Friend pointed to the spot, allowing Sercombe to crash home the penalty.
Then after the break Roofe took over, first when he picked up the ball on the corner of the penalty area.
The 23-year-old skipped inside his marker and took a couple of steps forward before guiding an unstoppable curler across Nordfeldt and into the far corner.
And worse was to follow for the Swans when they conceded a goal from their own corner just before the hour mark, Chris Maguire racing clear before feeding Roofe, whose shot hit Nordfeldt but looped up and bounced into the net.
Gomis pulled one back in the 66th minute with an angled finish after Jack Cork found him in the penalty area, but Swansea went back into their shell and Oxford were able to see out the game without any further drama to register a famous victory.