Two goals in the space of five second-half minutes from Steven MacLean and Tom Craddock did the trick for the U's as they also claimed their first win over the Bantams in the club's last eight meetings.
But it was the visitors who looked on course for three welcome points at the Kassam Stadium after midfield player David Syers gave Taylor's men a deserved ninth-minute lead.
"I felt at half-time we needed that second goal," said Taylor. "We didn't keep hold of the ball, which is disappointing.
"We had a brilliant opportunity to score a second when Omar Daley went through. He had an easy one really.
"But Oxford played very well. They're a team that get a lot of bodies forward.
"I can't fault the effort my players' effort, but we are having to work hard because we don't keep hold of the ball."
Victory for the U's saw them avenge their 5-0 whitewash at Valley Parade in October, much to the delight of their manager and former Bradford defender Chris Wilder.
Maclean forced the ball in from close range for a 77th-minute equaliser after James Constable's shot was saved by the legs of goalkeeper Lenny Pidgeley.
And Craddock then nodded in a winner at the far post on 83 minutes after Constable's driven cross from the right had just eluded MacLean.
Earlier, Syers struck from close range when Robbie Threlfall's corner was headed down by Richard Eckersley, for his seventh goal of the season.
City are now down to 14th.
Oxford United: Clarke, Tonkin, Wright, Batt, Worley, Hall (Heslop 58), McLaren, Clist, MacLean, Craddock (Sangare 89), Midson (Constable 58). Unused substitutes: Eastwood, Green, Payne, Deering
Bradford City: Pidgeley, Oliver, Eckersley, O'Brien, Threfall (Hanson 88), Kiernan, Daley (Speight 58), Bullock, Adeyemi, Syers, Cullen (Evans 46). Unused substitutes: Osborne, McLaughlan, Horne, Hunt.
Referee: D Phillips (West Sussex).
Man of the match: David Syers.
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