Goals from Steven Dovey, Scott Floyd and Miles Lynch handed the Pilgrims a 3-1 win at RAF College Cranwell.
Coalville reduced the arrears late on, but the Pilgrims held on to end a seven-match winless streak in league action.
Boston (4-3-3): Travis Portas; Daniel Worthington (Conor Allen 46), Billy Hodgkiss, Joe Cain (Daniel Moulds 46), Jack McCallum; Jack Dykes, Liam Moran, Corey Newman (Miles Lynch 46); Steven Dovey, Scott Floyd, Bradley Easey.