Burnley had two players sent off and then suffered the disappointment of losing on penalties as they crashed out of the FA Youth Cup.
Central defenders Bobby Thomas and Edon Pruti both saw red on a dramatic night at Turf Moor.
Thomas was dismissed in the aftermath of Oxford's 81st-minute equaliser as the third-round tie headed towards extra-time.
Pruti was then dismissed for handball to concede a penalty in the 110th-minute which Kai Calderbank-Park saved.
But the Clarets' keeper couldn't repeat the heroics in the shoot-out as Oxford clinched a fourth-round tie at home to Bournemouth or Mansfield Town.
Burnley had got off to a dream start as Michael Fowler took advantage of United goalkeeper Max Evans' error to slide the ball into an empty goal.
But they failed to press home that advantage and the U's - top of the Football League Youth Alliance's South-West division - deservedly levelled through substitute Ryan Crooks in the 81st-minute.
The Clarets almost snatched victory in added time with a Dan Moss strike that thundered against the underside of the bar.
But neither side could find another goal in the extra 30 minutes.
And even though the Clarets bravely hung on to take the tie to penalties, they couldn't complete the great escape as missed penalties from Matty Rain, Fowler and Ethan Kershaw saw Oxford progress.
After a quiet opening start to the game it was the Clarets that took the lead with eight minutes played as Fowler charged down an attempted clearance from Evans to slot home.
And despite being second best before the break, Burnley should have led 2-0 when Fowler created a chance for Kai Smith, who couldn't convert from eight yards out.
Smith then saw an effort cleared off the line just after the interval before Fowler shot over and then failed to get on the end of a low cross from super-sub Rhys Fenlon.
But a powerful Oxford side always carried a threat and with nine minutes to go made it 1-1 when the lively Crooks slotted home before clashing with Thomas.
Replays suggested it was a case of six of one, half-a-dozen of the other, but it was Thomas who was shown a red card for an apparent shove - to see Burnley reduced to 10 men.
That became nine when Pruti followed his defensive partner down the tunnel in the second half of extra-time when he kept out a goalbound header from Harry Sampford with an outstretched arm.
And even though Kyran Lofthouse wasn't able to immediately add to the punishment, Oxford's celebrations were only put on hold.
The outstanding Fenlon and Kian Yari scored for the Clarets in the shoot-out, but Rain and Kershaw saw their efforts saved and Fowler dragged his attempt wide of the target.
And with the Oxford trio of Fred Niblett, Crooks and Michael Elechi all hitting the target, Burnley fell at the first hurdle on a disappointing night.
Burnley: Calderbank-Park, Moss, Pruti, Thomas, Rain, Steels (Fenlon 61), Mupariwa (Yari 113), Kershaw, Smith (Richardson 113), Conn-Clarke (Patterson 82), Fowler. Substitute: Allen.
Oxford: Evans, Sampford (Stevens), Niblett, Jones, Elechi, Lofthouse, McCreadie, Chambers-Parillon (Goodrham), O James, Spasov (Edwards), Lopes (Crooks).