Crawley came from behind to record their sixth win in seven games and stay top of the table.
Oxford opened the scoring through Yemi Odubade's penalty, after he himself was brought down by Jake Wright.
But Crawley levelled midway through the first half with Jon-Paul Pittman's long-range shot past Ben Hinchliffe.
Five minutes later they were ahead when Jamie Cook headed home from 12 yards and only team-mate Adam Quinn's unwitting block denied Cook another.
Oxford Utd: Turley (Hinchliffe 27), Quinn, Willmott, Osborne, Clarke, Murray, Burnell, Evans (Guy 46), Haldane (Deering 57), Odubade, Trainer. Subs Not Used: Constable, Carruthers.
Goals: Odubade 17 pen.
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Booked: Pinault, Stevens.
Goals: Pittman 36, Cook 41.
Att: 3,992
Ref: R Fletcher (England).
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