The Pilgrims created and wasted a string of chances at the Horsfall Stadium and were beaten by Oli Johnson's 15th minute penalty following Ryan Qualter's foul.
United were particularly dominant after half-time, but arguably their best chances arrived in the first half when Nicky Walker cracked the crossbar with a free-kick and Jonny Margetts screwed the rebound wide.
Manager Craig Elliott had opted to make three changes ahead of kick-off, with Ben Davies making his full debut and Nathan Arnold missing out through injury.
Played in windy conditions in the wide expanse of the Horsfall Stadium, both sides struggled to make early headway but the hosts took the lead on the quarter hour mark.
Qualter felled Connor Branson in the box and JOHNSON blasted home the spot-kick despite George Willis guessing correctly.
United responded strongly and Adam Marriott’s free-kick looped up kindly off the Avenue wall for Margetts, but he got the ball stuck under his feet and fired straight at Steven Drench.
Walker’s ferocious free-kick soon rattled the underside of Drench’s crossbar and Margetts and Marriott got in each other’s way as they both attempted to guide home the rebound.
Marriott had a further left-footed effort fly into the side-netting as United’s dry spell in front of goal went on.
Jamie Spencer’s header clipped the outside of Willis’ post after the break, but Margetts had already been denied by Drench’s save from an Andi Thanoj corner, while a terrific ball from full debutant Davies skipped across goal without a crucial United touch.
The Pilgrims cranked up the pressure but failed to seriously trouble Drench in the Avenue goal. Jordan Gough’s effort deflected wide, Spencer Harris sent a header off target before Jonathan Wafula and debutant Cieron Keane teed up Craig Westcarr to drill an effort wide.
When ex-Pilgrim Shane Killock blocked heroically from sub Andre Johnson at the death, United knew the game was up and their goalless Bank Holiday weekend drew to a close.
Bradford PA (4-2-3-1): Steven Drench; Mark Ross, Gianluca Havern, Shane Killock, Nicky Clee; Connor Branson, Nicky Wroe; Lewis Knight (Adam Nowakowski 74), Jamie Spencer (Chris Dawson 67), Oli Johnson (Ryan Toulson 82); Jake Beesley. Subs (not used): Danny Boshell, Jack Atkinson (gk).
Boston (4-4-2): George Willis; Ben Davies, Ryan Qualter, Spencer Harris, Jordan Gough; Jonathan Wafula (Andre Johnson 80), Brad Abbott, Andi Thanoj, Nicky Walker; Adam Marriott (Craig Westcarr 60), Jonny Margetts (Cieron Keane 60). Subs (not used): Ben Middleton, Toby Lees.
Referee: Dean Hulme.
Attendance: 573.