Chelsea, fielding a near full-strength team, came through their home tie with League One Scunthorpe by two goals to nil.
There were more than 50 league positions between the clubs at the Kassam Stadium, where Oxford came from behind to lead 3-1 after Ecuador international Jefferson Montero had put Swansea ahead.
Liam Sercombe equalised from a penalty just before half-time and two goals in 10 minutes soon after the interval from Kemar Roofe put the home side in sight of victory.
Bafetimbi Gomis pulled one back for the Welsh club, who had made 10 changes from their last Premier League game, but Oxford held on.
“I thought the performance was outstanding, it was always going to be a difficult game against a Premier League side,” their manager Michael Appleton told BBC Sport.
“I don’t want to give Kemar Roofe too much praise but he’s done ever so well this year — we’re very used to seeing goals like his first one today in many games.
“This is reward for everyone at the football club but it’s really important to gain promotion and if we can improve on the squad it will stand us in good stead.”
Oxford, a top-flight team 30 years ago before dropping back into non-League football from 2006-10, are third in League Two, with the top three in May due to go up.
Roofe, who signed for them from West Bromwich Albion in the close season after a successful loan period, felt the triumph was down to his team’s efforts rather than any lack of application by Swansea.
“I don’t think they underestimated us, we were just on our game,” he said.
Alan Curtis, recently appointed Swansea manager until the end of the season, said his much-changed team had been “poor” for the first hour of the game.
“We made changes and there was a certain amount of rustiness but I am disappointed,” he told reporters.
“The team we picked was strong enough to win, but all credit to Oxford. They were the better team and deserved to win.
“The league was always going to be the priority but we wanted a cup run and to get some momentum going. It’s a huge setback for the club.
“We’re going to have to lift everyone for our next game.”
That match is a crucial Premier League fixture against fellow strugglers Sunderland on Wednesday.
Sunderland are bottom but one with 15 points and Swansea are two places ahead of them on 19 points.
Chelsea avoided a similar embarrassment to last season’s stunning 4-2 FA Cup defeat at home to Bradford City, although at times they made hard work of their tie against another third-tier side in Scunthorpe.
Spanish international Diego Costa put them ahead in the 13th minute from a cross by Branislav Ivanovic but the visitors rallied well in the second half and were furious to be denied a penalty when Ramires appeared to trip Kevin van Veen.
A few minutes later 19-year-old Londoner Ruben Loftus-Cheek, a half-time replacement for Oscar, scored his first goal for the club from Cesar Azpilicueta’s low centre.
Scunthorpe were denied a consolation goal when fullback Jordan Clarke’s fierce shot struck the post.
“It was not an easy game,” said Guus Hiddink, who is hoping to repeat his feat of 2009 by winning the FA Cup as Chelsea’s interim manager.
The experienced Dutchman told BT Sport he was particularly pleased with teenager Loftus-Cheek.
“We have these youngsters and I know them now after three or four weeks. When it’s an option I don’t hesitate to bring them (into the team).
“If you have an Academy, then you must bring the young players. But they must go to a certain level.”
[Source:- REAUTERS]