Three goals in 13 second half minutes completed the turnaround with 18-year-old Peter Bore, a local lad, coming off the bench to score twice on his debut.
The other Grimsby goal came from striker Isaiah Rankin on his return to the club, and he revelled after moving inside following the substitution of striker Michael Reddy by Bore.
Grimsby completely turned the game on its head with goals from Bore on 67 minutes, Rankin five minutes later and Bore again after 79 minutes from a Peter Beagrie corner which was not cleared.
Boston bossed the first half and might have scored inside two minutes when a Mark Greaves header hit the post and rolled along the line with keeper Phil Barnes, making his debut for Grimsby, nowhere.
It was no surprise when Francis Green beat the offside trap to slip the ball past Barnes after 16 minutes, and when last season's leading scorer Julian Joachim turned in a low cross by Paul Tait on 53 minutes the away win looked certain.
But Grimsby had other ideas, and after harsh words from new boss Graham Rodger at half-time they set about Boston with a vengeance. The first goal after 67 minutes came early enough to give them hope, and once Rankin had made it 2-2 five minutes later you sensed that a Grimsby victory was on the cards.
Rankin was denied by the crossbar following a wonderful effort from 25 yards, but Bore blasted in the winner with 11 minutes left to send the home fans into ecstasy.
Before the end many of the 600 Boston followers were making their way out of the ground unable to comprehend what they had seen.
it was an important victory for Grimsby, who face a tricky away visit to Wrexham and Northampton, whereas Boston now face two homes games and will be looking to build on their promising performance of the first hour or so.