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The Mariners looked a totally different side after manager Russell Slade introduced flu-hit striker Martin Gritton in the second half.
After trailing at the interval, they were back level just 50 seconds after the re-start thanks to a goal on his debut by Brentford striker Matt Harrold.
Harrold, who had joined on-loan only a few hours earlier, capitalised on a lack of concentration in the Oxford defence to loop a header over stranded goalkeeper Chris Tardif.
And with Gritton giving Harrold the support he needed up front, the Mariners were able to remain on the front foot throughout the second half.
Parkinson snatched the winner on 72 minutes when he broke Oxford's offside trap, cutting in from the left touchline before shooting past Tardif.
And although Oxford, who had controlled the first half, staged a late rally,
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Striker Tommy Mooney hit a long-range free-kick over the bar and in injury time he struck the post with a close-range shot, after inconsistent Town keeper Anthony Williams had dropped the ball.
Oxford had taken the lead 11 minutes before the break through Argentine midfielder Lucas Cominelli.
He rifled in a 25-yard shot after Mooney had deceived the Grimsby defence with a well-worked free-kick.
Oxford's management team from Argentina had begun the game with four South Americans for the first time.
Uruguayan Mateo Corbo returned to the defence, River Plate midfielder Juan Pablo Raponi was given his home debut and even the manager's son, Emiliano Diaz came on late in the match.
But this was a second successive defeat for Oxford, and they have effectively waved goodbye to any lingering play-off hopes. Meanwhile have Grimsby got them selves back on the Play-Off track.
Grimsby now lie in 12th place, 6 points behind 5th placed locals Lincoln City.