The Pilgrims were undone by Reece Styche's sixth minute strike as Billy Heath's team became the first Alfreton side to win at The Jakemans Stadium at the 14th attempt.
Jordan Slew failed to hit the target with United's two clearest openings in the first part of the Christmas and New Year double-header between the sides.
Alfreton took the lead in the sixth minute when STYCHE controlled ex-Pilgrim James Clifton’s long throw and slammed the ball past George Willis from 12 yards.
The Reds looked well set to take a two-goal advantage when Tom Allan headed goalwards following Clifton’s cross from the right but Willis stuck out a leg to produce a phenomenal save.
Willis made a further save with his legs to thwart Curtis Bateson as the half ticked by.
United’s best chance of the first half fell to Slew in stoppage time but he blasted into the side-netting.
Styche clipped the Boston crossbar after the break before United crafted a great chance for Slew, with Max Wright crossing from the right flank, but the finish was too high from 10 yards.
Alfreton keeper Sam Ramsbottom produced a fine stop to thwart Nicky Walker at the mid-point of the second half, with Josh Wilde doing enough to prod the loose ball away from the onrushing Wright, but the Pilgrims failed to muster another meaningful effort.
Boston (4-3-3): George Willis; Ben Davies, Ryan Qualter, Spencer Harris, Ashley Jackson; Brad Abbott, Andi Thanoj, Jonathan Wafula (Danny Rowe 85); Max Wright, Jordan Slew (Jay Rollins 70), Nicky Walker. Subs (not used): Lewis Gibbens, Sebastian Malkowski (gk).
Alfreton (4-2-3-1): Sam Ramsbottom, James Clifton, Luke Shiels, Adam Curry (Nathan Hotte 75), Josh Wilde; David Lynch, Tom Platt; Reece Styche (Jordan Sinnott 83), Tom Allan, Curtis Bateson; Richard Peniket. Subs (not used): Callum Chettle, Tom Nicholson (gk).
Referee: Tom Parsons.
Attendance: 1,393 (56 visitors).