The Pilgrims went down to Liam Hearn's 41st minute header after seeing numerous chances go begging.
Louis Briscoe rattled the post with a first half free-kick and Mani Dieseruvwe, Josh Robinson and Nat Brown were all denied by goalline clearances in a frantic spell towards the end of proceedings.
Briscoe’s ferocious 18th minute set-piece bounced to safety, with Josh Robinson agonisingly unable to convert the rebound, as United started brightly.
Alfreton countered with Mark Shelton getting into a glorious shooting opportunity but his eventual drive was high and wide.
Jay Rollins was at the forefront of much of United’s first half play and he slammed an effort wide following a partially-cleared corner.
Alfreton took the lead four minutes before half-time when Jordan Richards’ fabulous cross from the right was headed home by HEARN at the near post.
Substitute Alex Simmons crashed a drive straight down the throat of ex-Pilgrim Fabian Spiess shortly after coming off the bench, while the Alfreton stopper denied Robinson moments later.
The game’s defining moment arrived in the 83rd minute with Monkhouse hacking Dieseruvwe’s drive off the line before getting back in the nick of time to divert Robinson’s goalbound volley over the bar with his head. The resulting corner saw Brown thwarted on the line by Hartlepool United loanee Richards.
Alfreton (4-3-3): Fabian Spiess; Jordan Richards, Brad McGowan, Todd Jordan, Ryan Wilson; Wes Atkinson, Mark Shelton, Andy Monkhouse; Craig Westcarr (Callum McFadzean 73), Liam Hearn, Sam Smith. Subs (not used): Paul Marshall, Morgan Brough, Ellis Evans.
Boston (4-3-3): Ross Durrant; Josh Robinson, Tom Batchelor, Nat Brown, Jan Yeomans; Harry Vince, Adam Chapman, Lewis Hilliard (Mani Dieseruvwe 53); Jay Rollins, Colby Bishop, Louis Briscoe (Alex Simmons 60). Subs (not used): Shane Clarke, Kalern Thomas, Charlie Gatter.
Referee: Paul Graham.
Attendance: 547.