fore Ben Sayer's 109th minute winner from long-range saw the Magpies through to the next round 2-1.
Newcastle edged the first-half with Grimsby Town goalkeeper Rob Peet at his best to keep them out with a string of fine saves.
But he conceded in the final minute of the first period when Aaron Spear hammered home.
Town came out fighting after the break and won a penalty when Keiron Smith was brought down in the box, but Ryan O'Loughlin saw his kick saved by Jak Alnwick.
Town were level on 67 minutes, however, when Sam Mulready pounced to rifle home low.
It remained 1-1 into extra-time when Sayer chipped over Peet from 25 yards to take Newcastle to a showdown with the Mancs.