Lee Beeson doubled his season’s tally of goals to keep up the Poachers’ impressive away form.
He could have had a hat-trick after seeing his first half penalty saved.
The spot-kick was awarded midway through the first half when Pinchbeck’s Ben Robson handled Luke White’s effort on the line.
Although Alex Smith managed to keep out Beeson’s penalty, Robson was red-carded, leaving the home side with an uphill battle.
Beeson scored with a low shot 10 minutes later to give the visitors a 1-0 interval lead, only for Pinchbeck to equalise soon after the restart with a penalty of their own – Jack Fixter converting after Jordan Tate fouled Fin Armond.
But Beeson scored a screamer eight minutes later – his fourth of the season – to restore Boston’s lead. Abou Sylla smashed home a third after 74 minutes to the seal the points.
With the top four all in FA Vase action, Gary Edgley’s side were able to close the gap, moving level on points with 4th-placed Loughborough Students and three behind 3rd-placed Anstey Nomads., with a game in hand on both.
The Boston Town boss admitted it wasn’t his side’s best performance of the season. But he added: “On a tough surface to play any football on, we did what we had to do. The moments of quality were all three goals.”