The extra time was played because Peterborough goalkeeper Mark Tyler was carried off 15 minutes from time after a sickening collision with Grimsby striker Michael Reddy.
United striker Richard Logan went in goal but was never seriously tested despite some desperate Grimsby pressure.
It had seemed a long time since Grimsby had opened brightly and took a deserved 28th minute lead.
Striker Junior Mendes, making his home debut, found fellow striker Reddy and although his shot took a deflection it beat Tyler for his 11th goal of the season.
But Grimsby were unable to enjoy their lead for long as within two minutes some slack defending enabled creative midfielder Peter Gain to waltz through a static defence and slot the ball in.
And in added time at the end of the first half Gain almost put Peterborough ahead when, with keeper Steve Mildenhall standing out of goal, Gain's shot at the open net saw the ball strike the post and bounce away.
Grimsby came out determined for the second half but were caught by a sucker punch on 71 minutes.
Logan put over an inch-perfect cross which was expertly glanced home with his head by leading scorer Danny Crow.
Five minutes later came the collision which saw Tyler carried off with a concussion.
And despite throwing all their men forward including keeper Mildenhall in the closing stages for set pieces, Grimsby were unable to get the equaliser.