Chelsea, fielding a near full-strength team, came through their home tie with League One Scunthorpe by two goals to nil and Tottenham Hotspur needed a controversial late penalty by Harry Kane to draw 2-2 at home to Leicester City.
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.
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.
“It’s a huge setback for the club,” he told reporters. “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 has been unbeaten in four games since taking charge again after Jose Mourinho was sacked.
He told reporters that Costa was “doubtful” for Wednesday’s game at home to West Bromwich Albion as the Premier League champions seek to improve on their poor defence of the title.
Claudio Ranieri’s Leicester were denied a repeat of last season’s 2-1 FA Cup win at Tottenham in an exciting tie at White Hart Lane, after the teams, who meet in the Premier League on Wednesday, made 15 changes between them.
Spurs held the lead for only nine minutes after Christian Eriksen scored early on, Polish defender Marcin Wasilewski equalising with a header.
Japan’s Shinji Okazaki then scored only two minutes after coming on as a substitute at the interval.
The home side threw on England internationals Harry Kane and Dele Alli and Kane’s penalty for handball by Nathan Dyer, his 50th goal for the club, earned them a replay.
“I’m very pleased with our performance,” said Ranieri, who declined to complain about the penalty award.