United trailed 2-0 to Ashley Hemmings and Sam Austin goals by the time Elliott plundered his 21st goal of the season with 20 minutes to play at Aggborough.
Amari Morgan-Smith sealed victory for Harriers five minutes later against a United side missing the services of their ill manager Paul Cox.
John Ramshaw took charge of the Pilgrims for the first time and he saw his side deliver a resolute first half showing against the in-form Harriers.
United trailed at the break courtesy of an ex-Pilgrim - with HEMMINGS crunching home a 22-yarder in the 27th minute after being afforded too much time to pick his spot.
Harriers doubled their lead with 18 minutes on the clock in the second period, with AUSTIN waltzing through to beat Dewhurst with a fine reverse finish.
United rallied and cut the deficit seven minutes later. Fit-again substitute James Hanson was instrumental, forcing Luke Simpson into a smart save, and ELLIOTT tucked home the rebound.
Boston's hopes of snatching a point were dashed when Caleb Richards' cross from the left was powered home by the head of MORGAN-SMITH in the 75th minute.
Kidderminster (4-2-3-1): Luke Simpson; Alex Penny, Keith Lowe, Nathan Cameron, Caleb Richards; Lewis Montrose, Mark Carrington; Ashley Hemmings, Sam Austin (Jaiden White 90), Omari Sterling (Ethan Freemantle 90); Amari Morgan-Smith. Subs (not used): Joe Foulkes, Keziah Martin, Devonte Redmond.
Boston (4-3-3): Marcus Dewhurst; Matt Tootle (Keenan Ferguson 88), Luke Shiels, Scott Garner, Scott Duxbury (James Hanson 66); Brad Abbott (Jordan Preston 84), Tom Platt, Shane Byrne; Fraser Preston, Danny Elliott, Joe Leesley. Subs (not used): Connor Dimaio, Ben Sault.
Referee: Jonathan Maskrey.
Attendance: 2,823 (49 visitors).
PIC: Ade Hoskins.