Stuart Anderson's extra-time penalty booked Salisbury a place in the FA Cup third round for the first time in their history with victory at Grimsby.
Dan Fitchett curler gave the visitors the lead, before Rob Duffy's injury-time header forced extra-time.
Duffy scored again seconds after the restart but Brian Dutton's close-range header brought Salisbury level.
Shaun Pearson hauled down Fitchett and Anderson scored from the spot to book a third-round tie at Sheffield United.
VIEWS FROM THE DRESSING ROOM
Salisbury City manager Darrell Clarke told BBC Wiltshire:
"The belief in my players that we could win this game was fantastic. The boys were unbelievable and no one in this stadium can say we didn't deserve it.
"We had a game plan and it worked superbly so we are really pleased for everyone at the football club.
"I am proud as punch of my boys tonight. It's the first time in our history we have reached the third round. I want to thank the fans who have come down in their coach-loads."
Grimsby Town joint manager Paul Hurst told BBC Radio Humberside:
"Taking nothing away from Salisbury, who were worthy winners on the night, but we didn't really ask them any questions and they ran out winners and we can't have any arguments with that.
"It was almost as though we turned up expecting to win.
"I've seen players do things tonight, or attempt things, that, with all due respect, you see on a Sunday league pitch."