Jake Wright Jnr opened the scoring in the 12th minute before Danny Elliott - on for the injured Jordan Burrow - bagged a brace in the 29th and 59th minutes.
Jaiden White replied for the visitors, but Jordan Preston added a fourth in the 80th minute to seal United's safe progress.
United's starting XI was unchanged to the previous week's against Harriers - except for Preston replacing the injured Paul Green.
The Pilgrims took the lead when Joe Leesley delivered a pinpoint corner and WRIGHT JNR glanced home his fifth successive home goal for United.
United lost the services of Burrow to a calf injury shortly afterward - but replacement ELLIOTT drove the Pilgrims into a 2-0 lead with a left-footed finish on the end of Keenan Ferguson's assist from the right.
The Pilgrims effectively sealed their progress 14 minutes after half-time when ELLIOTT got on the end of Matt Tootle's clearance to outmanoeuvre Keith Lowe and run on to round Luke Simpson and angle home a low finish into an unguarded net.
Kidderminster rallied and substitute WHITE reduced the arrears after Alex Penny had hit the post following Ashley Hemmings' corner.
Harriers wanted a penalty for a possible foul on Ethan Freemantle but United survived without any further scares - with PRESTON adding the icing to the cake with a driven finish from 12 yards after Lowe had only been able to partially block Ferguson's low cross.
Boston (3-5-2): Marcus Dewhurst; Kyron Gordon, Luke Shiels, Matt Tootle; Keenan Ferguson, Jordan Preston, Tom Platt, Shane Byrne, Joe Leesley (Scott Duxbury 83); Jordan Burrow (Danny Elliott 22), Jake Wright Jnr (Fraser Preston 82). Subs (not used): Scott Garner, Finlay Armond, Milan Lalkovic, Peter Crook (gk).
Kidderminster (4-2-3-1): Luke Simpson; Alex Penny (Joe Foulkes 69), Geraldo Bajrami, Keith Lowe, Caleb Richards; Lewis Montrose, Elliot Bonds; Ashley Hemmings, Sam Austin (Jaiden White 63), Keziah Martin (Omari Sterling 77); Ethan Freemantle. Subs (not used): Nathan Cameron, Mark Carrington, Amari Morgan-Smith, Jamie Emery (gk).
Referee: Matthew Scholes.
Attendance: 975 (48 visitors).
PIC: Russell Dossett.