The Pilgrims took a fourth minute lead through Harry Vince's penalty following a foul on Jack Brown.
Bradford prevailed after equalising through Ville Moilanen on 24 minutes and Curtis Peters two minutes after the break.
Boston (4-3-3): Harry Payne; James Gordon, Jack Withers, Bailey Forth, Callum Rodger; Jordan Tate, Harry Vince, Peter Evison; Ben Lawrence, George Hobbins (George Smith 63), Jack Brown (Haydn Havard 55). Subs (not used): Oli Drummond, Connor Stocks, Jenson Ball.
Referee: Daniel Issawi.
Attendance: 305.