Anthony Dudley's goal on the half-hour mark proved to be the difference on Tuesday evening.
It ensured a losing start for Boston`s caretaker-manager Karl Hawley, although the Pilgrims more than held their own against their promotion-chasing visitors.
The only other game on the night saw Chorley and Tamworth share a 1-1 draw at Victory Park.
The point apiece leaves the Magpies and the Lambs in sixth and seventh place respectively.
Josh O'Keefe's first goal of the season for Chorley after 52 minutes cancelled out Darryl Knights 47th minute opener for the visitors.
But the draw was enough to extend Matt Jansen's side`s unbeaten home record to eight games.