The Mariners ultimately proved too strong at The Jakemans Stadium and prevailed courtesy of a double strike from Padraig Amond and a header from ex-Pilgrim Shaun Pearson.
Kaine Felix had drawn United level two minutes into the second half, but Grimsby's quality shone through to clinch a deserved victory.
Boston (4-4-2): Henrich Ravas; Zak Mills, Scott Garner, Carl Piergianni, Liam Marrs; Kaine Felix (Cameron Johnson 85), Kyle Dixon, Jordan Deacey (Jake Sheridan 76), Jay Rollins (Kingsley Ogbodo 42); Dayle Southwell (Jack Friend 85), Mark Jones (Harry Limb 85).
Referee: Steve Ross.
Attendance: 1,037 (432 visitors).