The former Tranmere striker turned the ball home at the near post two minutes into the second period to earn Town a sixth successive away victory.
Jones had missed a great chance in the first half at London Road, but he atoned in fine style when converting a cross from striker partner Michael Reddy.
But this success was down to a tremendous defensive effort from Russell Slade's side as they absorbed a torrent of pressure from the hosts.
Grimsby keeper Steve Mildenhall was a magnet-like figure in the first half as the ball seemed attracted to him while Posh piled on the pressure.
Mildenhall was in the right place to block two long-range efforts from James Quinn before also thwarting Adam Newton who unleashed a half-volley from the edge of the box after a poorly cleared Sagi Burton corner dropped into his path.
And even when Mildenhall wasn't proving a formidable last line of defence, Posh saw good chances go agonisingly wide.
David Farrell hooked over inside the opening 60 seconds, Burton delivered a pinpoint cross which was steered wide by Quinn's head and an angled effort from Peter Gain shaved the paint on its way past the outside of the far post.
Veteran Grimsby full-back John McDermott brought the curtain down on the opening half by attempting to cap his 600th league appearance for the club with a rare goal, but he dragged a 20-yard drive well wide of Mark Tyler's goal.
And following Jones' goal, the second half followed the same pattern of Posh pressure but no end product.
Winger Adam Newton was guilty of wasting arguably the best opening of all when dragging a shot tamely wide following the move of the match on the hour before captain Dean Holden blazed wildly over deep into stoppage time as Grimsby left with the points.