County looked to be heading for a third successive victory after skipper Julien Baudet climbed high to head home Paul Bolland's right-wing cross after 27 minutes.
They might have been even further in front because Oxford keeper Chris Tardif made a brilliant double save to deny Glynn Hurst.
Hurst really should have scored or at least squared the ball to an unmarked Mark Stallard to his right.
Oxford had been poor in the first half and they looked to be in disarray when centre-back Paul Wanless went off with concussion early in the second half.
But striker Mooney dropped back to play at centre-half, something he had done at previous clubs Watford and Derby.
County then shot themselves in the foot with Bolland handling a right-wing cross by Chris Hackett with 15 minutes remaining. Mooney strode forward to convert the penalty for the equaliser.
Seven minutes later Baudet was adjudged to have brought down substitute Craig Davies just inside the box and Mooney again sent goalkeeper Saul Deeney the wrong way from the spot.
It was the first time this season that Oxford had come from behind to win.