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Hargreaves, a striker in his Grimsby days but now operating in midfield, got away from his former club's defence and placed a fine header beyond keeper Steve Mildenhall.
There were just two minutes left on the clock and it looked at that point as if a rare 61st minute goal by central defender Tony Crane from a Tom Newey corner was going to win it for the Mariners.
Grimsby looked to be in control after taking the lead but when Newey picked up a yellow card for a silly foul, he was doubly punished when Chris Hackett's free-kick was headed home.
The game came to life early in the second-half after a fairly dour opening period in which Grimsby only started to play towards half-time.
There were a few chances at either end early in the second-half in a tight match which never looked like producing many goals.
In the second-half Oxford striker Steve Basham shot over from a good chance and then a Lee Bradbury header was turned aside by Mildenhall.
At the other end striker Martin Gritton headed over and then Grimsby striker Michael Reddy, whose skill and pace troubled Oxford throughout, shot over.
The highlight of the first-half had come from Reddy who drifted past several defenders and brought the best out of Oxford keeper Billy Turley, who was making his debut.
But it was a typical opening day game with neither side wanting to commit themselves too much and risk losing.
In the end both sides were probably pleased with a point, although by conceding late on Grimsby were no doubt the unhappier of the two sides.