The Pilgrims went down 4-2 to Preston North End (Myerscough).
Withers and Drummond were both on target but the Pilgrims, missing a clutch of regular players, came up short on their long trip to Lancashire.
Boston (4-3-3): Harry Payne; Ben Lawrence, Jack Withers, Callum Rodger, Jack Brown (Arkadiusz Michalczyk 86); Jordan Tate, George Hobbins, Oli Drummond (Jenson Ball 66); Peter Evison, Liam Adams, Haydn Havard.