Charman finished off an incisive move involving Nick Haughton and Dan Pike as Adam Murray's side maintained their position as title favourites.
United's clearest chance fell to Sam McLintock before half-time - but the midfielder sailed an effort narrowly wide.
United boss Ian Culverhouse had made four changes ahead of kick-off, with Ethan Sephton ruled out with an ankle injury, while Jake Wright was deemed only fit enough for the bench after a bout of illness.
Cameron Gregory made an early save with his legs to deny CHARMAN, but was powerless to stop the same player sweeping the Coasters into the lead following Haughton's switch of play for Pike to cross from the Fylde right.
United responded with Tom Nixon lifting an effort too high and McLintock firing marginally wide - either side of the excellent Emeka Obi's header glancing wide from a Haughton corner.
Gregory palmed aside a Haughton free-kick before half-time, with Haughton again narrowly missing the target with a second half set-piece, as the Pilgrims found Fylde a tough nut to crack.
Lirak Hasani and Finley Thorndike were both introduced as United chased a leveller, with Wright following 10 minutes from time, but Murray's men held on to retain their slender advantage in the title race.
Boston (4-1-2-1-2): Cameron Gregory; Tom Nixon, Luke Shiels, Ben Pollock, Keenan Ferguson (Jake Wright 80); Tom Platt; Zak Mills, Will Atkinson (Lirak Hasani 65); Sam McLintock (Finley Thorndike 75); Jordan Burrow, Billy Chadwick. Subs (not used): Tre Mitford, Jo Cummings.
AFC Fylde (3-4-2-1): Chris Neal; Emeka Obi, Harry Davis, Alex Whitmore; Dan Pike, Danny Philliskirk (Will Hatfield 59), Danny Whitehead, Luke Conlan; Nick Haughton (Nathan Delfouneso 83), Joe Rowley; Luke Charman (Connor Barrett 90). Subs (not used): Bartosz Cybulski, Tom Walker.
Referee: Emily Heaslip.
Attendance: 1,636 (51 visitors).
PIC: Nikolay Hristov.