The Pilgrims were excellent in the first half hour at the Jakemans Community Stadium but failed to make a breakthrough - and Tamworth came back with a vengeance.
Michael Bostwick's own goal eight minutes after the break set the Lambs on their way and Ben Acquaye doubled their lead with 14 minutes to play.
United flew out of the blocks, just as they had done against South Shields at the weekend, but they could not make their early dominance count. Brad Nicholson had a fierce drive beaten aside by Jas Singh - but it was the Tamworth stopper's only meaningful save of the first half.
Tamworth came on strongly in the closing stages of the half, with Kyle Finn and Dan Creaney going close, but the scoreline remained deadlocked at the break.
The visitors were in front eight minutes after half-time when BOSTWICK grappled with Nathan Tshikuna as Jordan Cullinane-Liburd's long throw came into the penalty area - and got the decisive touch to send the ball spinning past Gregory and into the net.
United had a huge chance in the 71st minute when Keaton Ward motored through - but Singh stood up well to beat aside his effort.
Singh's save proved decisive, with ACQUAYE subsequently lashing home a partially-cleared Tamworth corner five minutes later.
Tempers flared - with United assistant boss Paul Bastock dismissed from the dugout - as the Lambs closed out their victory without too many scares.
Boston (4-1-2-1-2): Cameron Gregory; Zak Mills, Michael Bostwick, Tom Leak, Brad Nicholson; Martin Woods; Jordan Richards (Oliver Wilson 78), Keziah Martin (Tom Edge 67); Sam McLintock (Michael Gyasi 62); Keaton Ward, Jimmy Knowles. Subs (not used): Tyler Knowles, Jake Lovelace (gk).
Tamworth (4-2-3-1): Jas Singh; Matt Curley, Jordan Cullinane-Liburd, Liam Dolman, Callum Cockerill-Mollett; Ben Milnes, Jamie Jellis; Kyle Finn (Dempsey Arlott-John 90), Nathan Tshikuna, Ben Acquaye; Dan Creaney (Alex Jones 88). Subs (not used): Ty Deacon, Jamie Willets, Leon Phillips (gk).
Referee: Alex Sawden.
Attendance: 1,662 (91 visitors).
PIC: Russell Dossett.