Boston were guilty of missing some good chances and paid the price on 71 when Grimsby top scorer Michael Reddy got his 13th goal of the season.
It was his fourth goal in successive games as his shot took a wicked deflection before finding its way past keeper Conrad Logan.
One man who missed the goal was Boston boss Steve Evans, who was ejected from the ground with a police escort after blowing his top on the touchline.
Grimsby rode their luck at times and Boston striker Julian Joachim should have levelled in added time.
The much-travelled striker scored a late equaliser in the game at Boston, but this time he sliced wide when he should have scored.
Because of injury and suspension Grimsby were down to the bare minimum and for the first half they looked like a pack of strangers as Boston were in control.
Boston took control with Jamie Clarke having a good shot saved early on by Steve Mildenhall.
James Keene and sub Simon Rusk also squandered good chances and in the second half Chris Holland had a simple chance from a corner but shot over.
All three previous league meetings between these sides ended 1-1 and this looked to be heading for another draw before Reddy stepped in with the decisive strike.
Grimsby now face successive away games at Mansfield and Rochdale, but with their good away form they will relish the challenge as they look to push on in the title race.