The Pilgrims accounted for Loughborough Dynamo at the Nanpantan Sports Ground in their first outing since December 6.
Martyn Bunce's side took all three points when Tate converted Leighton Boughen's 21st minute cross.
Boston (4-3-3): Oliver Swaby (Seth Greeves 46); Jack Brown, Taylor Gray, Callum Rodger, Sarok Ali; Jack Henton (Jenson Ball 46), Jordan Tate, Peter Evison; Marshall Young, Jenson Bark, Leighton Boughen. Subs (not used): Arkadiusz Michalczyk, Harrison Holland.