The Mariners dominated the first half and took the lead when striker Colin Cramb coolly finished in the 18th minute after a throughball from French midfielder Thomas Pinault had thrown the Oxford defence into panic mode.
But an injury to Cramb unsettled Grimsby although substitute striker Darren Mansaram set up what should have been a decisive second goal early in the second half.
Mansaram crossed low from the right and midfielder Dean Gordon only had to touch the ball in at the far post. But he did not get a decisive enough touch on the ball and impressive keeper Bradie Clarke, playing only his second league game, was able to grab the ball on the line.
Oxford hit back with a well-worked equaliser in the 51st minute involving the experience of skipper Lee Bradbury and striker Tommy Mooney. When Bradbury's shot came back off the bar Mooney turned it in.
Grimsby could have grabbed a winner when a Gordon free-kick crashed against the bar but it was Oxford who finished the stronger and they could easily have grabbed all three points as the Grimsby defence frequently panicked.
In the end it was a better point for Oxford especially considering Grimsby's excellent home record and continued the good start for new Argentinian boss Ramon Diaz.
The Grimsby fans grew more and more disenchanted with their team as the game wore on and it certainly wasn't the early Christmas present they were looking for.