Chances were at a premium at the Brewery Field - although United were indebted to Cameron Gregory for fine saves to deny Glen Taylor and Sam Fielding in the second half.
United's best chance saw Martin Woods' stinging free-kick beaten aside by James Montgomery.
Ahead of kick-off, United boss Ian Culverhouse had omitted Jimmy Knowles from his starting XI for the first time this season. With Ethan Sephton missing out through injury, Jai Rowe and Dylan Hill were their two replacements.
In a fixture played two weeks later than originally scheduled, the first half passed by without any particularly noteworthy chances for either side.
After the break, United were forced into their first change when Zak Mills limped off, to be replaced by fit-again Tom Leak.
Kelsey Mooney found himself through on goal, only to be flattened by Mark Anderson at the cost of a booking, and Woods' firm free-kick was well repelled by Montgomery.
Spennymoor came alive and Taylor, looking to add to his eight previous goals against the Pilgrims, had a close-range effort blocked by Nicholson before forcing a save from Gregory.
Gregory subsequently excelled to keep out Fielding's ferocious drive following a partially-cleared corner.
There was a late scare when Brad Nicholson had to hook the ball off his own line from an Anderson cross-shot, but United held on.
Spennymoor (4-2-2-2): James Montgomery; Keenan Ferguson, Lebrun Mbeka, Reece Staunton (Ben Hockenhull 89), Owen Gallacher; Danny Mark Anderson, Sam Fielding; Danny Greenfield (Corey McKeown 89), Rob Ramshaw; Glen Taylor, Will Harris. Subs (not used): Callum Ross, Dan Atkinson, Riley Mouat.
Boston (3-4-2-1): Cameron Gregory; Zak Mills (Tom Leak 56), Michael Bostwick, Brad Nicholson; Jai Rowe, Jordan Richards, Martin Woods, Dylan Hill; Keaton Ward (Jimmy Knowles 63), Keziah Martin; Kelsey Mooney. Subs (not used): Tom Edge, Sam Essien, Tyler Knowles.
Referee: James Bancroft.
Attendance: 1,236.
PIC: Mark Fletcher.