The Pilgrims eliminated Kidderminster Harriers on their own turf following Danny Elliott’s 45th minute opener and an own goal from ex-United defender Alex Penny with 14 minutes remaining.
Ex-Pilgrim Ashley Hemmings had levelled the tie for the hosts after 65 minutes - but United showed plenty of resolve to book a trip to AFC Fylde in the semi-finals on Sunday.
The early stages were notable for blood injuries affecting the hosts' Nathan Cameron initially and then Harriers keeper Luke Simpson and United defender Scott Duxbury - the latter of whom was unable to continue following a serious facial injury.
Amari Morgan-Smith lifted an effort too high for Harriers, with Jake Wright Jnr firing into the ground and over the bar, while Elliott headed wide from a Shane Byrne cross.
United took the lead in the 45th minute when Simpson excelled to deny Brad Abbott and once substitute Keenan Ferguson had recycled the loose ball, ELLIOTT slammed home at the near post.
Marcus Dewhurst made a magnificent save to deny Hemmings' header at the beginning of the second half - but HEMMINGS did draw Kidderminster level in the 65th minute with a fine rising finish high to the United keeper's right.
United ultimately won the contest in bizarre circumstances, with PENNY and keeper Simpson somehow contriving to allow Wright Jnr's cross-shot to creep over the line.
The outstanding Femi Seriki went close to a late third, forcing Simpson into a smart save, moments after Omari Sterling had fired a dipping free-kick off target for the hosts.
Kidderminster (4-2-3-1): Luke Simpson; Joe Foulkes, Nathan Cameron, Alex Penny, Caleb Richards; Mark Carrington (Ethan Freemantle 86), Geraldo Bajrami; Ashley Hemmings, Keziah Martin, Omari Sterling; Amari Morgan-Smith. Subs (not used): Keith Lowe, Lewis Montrose, Jaiden White, Tom Palmer (gk).
Boston (3-5-2): Marcus Dewhurst; Scott Garner, Luke Shiels, Jake Wright Snr; Femi Seriki, Brad Abbott, Shane Byrne, Paul Green, Scott Duxbury (Keenan Ferguson 23); Jake Wright Jnr (Ntumba Massanka 79), Danny Elliott. Subs (not used): Andi Thanoj, Connor Dimaio, Fraser Preston.
Referee: Aaron Bannister.
Attendance: 3,921 (408 visitors).
PIC: Oliver Atkin.