Two goals from home midfielder Rhys Lewis handed the Gingerbreads a deserved victory over the Pilgrims who made 11 changes to the side beaten at Worcester City on Saturday.
The home side were worthy winners as an experimental United line-up failed to sparkle.
The brightest points of the United performance were arguably delivered by teenagers Lewis Sturman at right-back and James Reed in midfield.
Grantham were on the front foot in the opening stages, with Ricky Drury excelling to keep out a Lewis drive before Lee Canoville turned the loose ball to safety.
Drury also denied Gio Carchedi but the Gingerbreads were soon in front. Lee Potts crossed from the left and LEWIS finished well from 12 yards.
Grantham continued to create the better chances with Drury denying Sam Saunders and Carchedi's shot being deflected wide.
Town dominated at the beginning of the second half with Drury using his legs to keep out a Sean Cann drive, while Lewis sent a header wide from a Saunders free-kick.
The home side doubled their lead on 69 minutes when poor defending from the Pilgrims allowed LEWIS the time to add his second from close-range.
United's only notable shot on target saw Chris Hall's free-kick gathered by keeper Rob Murray.
Grantham (4-4-2): Rob Murray; Sam Purcicoe, Phil Watt, Sam Saunders, Lee Potts (Paul Grimes 81); Rhys Lewis, Grant Brindley, Chris Glarvey, Gio Carchedi (Damien Magee 58); Tony Battersby, Sean Cann (Jamie McGhee 71). Subs (not used): Ben Saunders, Martin Ball.
Boston (4-3-3): Ricky Drury; Lewis Sturman, Lee Canoville, Kevin Austin, Jason Field (Scott Dawson 58); James Reed, Chris Hall, Richard Jackson (Liam Ogden 46); Tom Sergeant, Leon Constantine, Tony Edwards (Charley Sanders 68). Subs (not used): Jason Lee, Andy Hewitt (gk).
Referee: Nigel Smith