As well as giving Culverhouse the perfect start, it extended United's brilliant record against Buxton to 22 wins and six draws from 29 encounters contested.
Culverhouse brought Luke Shiels and Zak Mills back into the United starting XI - and Mills almost opened the scoring in the second minute with an audacious chip which Theo Richardson palmed to safety.
Sam Long was called into action at the other end - denying Diego De Girolamo with a fine stop as Buxton threatened an early breakthrough.
Crawford drove the Pilgrims into a 30th minute lead, with the goal initially disallowed for offside, but re-instated by referee Abigail Byrne after noticing the final play of the ball had come from a Buxton player.
Richardson made another good save to deny Crawford a quickfire second, but the Pilgrims were soon two goals to the good. Scott Pollock got clear down the left-hand side to pull the ball back for Crawford to slam home at the near post.
Crawford was again thwarted by Richardson at the beginning of the second half but United were undeterred, with Scott Pollock rifling home from 18 yards to hand the hosts an unassailable lead.
Buxton tried to get themselves back into contention, but United were resolute throughout a determined second half display, with Long untroubled in the home goal.
Boston (4-1-2-1-2): Sam Long; Keenan Ferguson, Luke Shiels, Ben Pollock, Alex Brown; Joe Leesley; Zak Mills (Jean Leroy Belehouan 73), Will Atkinson; Scott Pollock; Byron Harrison (Jake Wright 61), Jordon Crawford (Micah Obiero 77). Subs (not used): Ellis Myles, Rhys Davies (gk).
Buxton (3-5-2): Theo Richardson; Levi Andoh (Luke Burke 55), Shaun Brisley, Sean Newton; Declan Poole (Harry Bunn 55), Connor Kirby, Jake Moult, Matt Sargent, Warren Clarke; Serhat Tasdemir (Zac Dearnley 78), Diego De Girolamo. Subs (not used): Lindon Meikle, Ollie Greaves.
Referee: Abigail Byrne.
Attendance: 1,450 (40 visitors).