Akwasi Asante and Anthony Dudley had the hosts in charge at half-time, despite Gavin Allott and Nicky Walker both rattling the post for United in near identical circumstances.
Second half efforts from Craig Mahon and George Waring subsequently sandwiched Ben Davies' free-kick for the Pilgrims as the home side ran out convincing winners.
United’s afternoon got off to a controversial start when Jay Rollins was cautioned inside four minutes for alleged simulation, after falling under a challenge in the Chester box.
Allott smacked the post with an angled effort a minute later as United came within a whisker of taking an early lead.
Ryan Qualter made fine blocks to deny Dudley either side of a flying George Willis save to thwart Mahon.
Chester took the lead in the 21st minute when Mahon’s deep corner was returned by Gary Roberts and Steve Howson’s header was helped home by ASANTE from close-range.
Walker became the second Pilgrim to hit the woodwork when his angled effort rebounded to safety off the far post.
Nicky Wroe subsequently clipped Allott into the clear but he dragged his effort across goal and wide of the far post.
Chester doubled their advantage two minutes before the break when Mahon skipped away from Davies and Qualter to allow DUDLEY to lift home a rising effort from inside the penalty area.
The Blues extended their lead in the 62nd minute when Grant Shenton’s long free-kick bounced across the United area and MAHON finished well beyond Willis.
United were afforded a route back into proceedings when Danny Livesey hacked down Rollins and DAVIES curled home a fine free-kick from 20 yards.
The visitors’ hopes of a comeback were immediately extinguished when Dan Mooney whipped in a cross from the right and WARING dived to head home from close-range.
Chester (4-4-2): Grant Shenton; Brad Jackson, Danny Livesey, Steve Howson, Matthew Waters; Dan Mooney (Lloyd Marsh-Hughes 84), Scott Burton, Gary Roberts (George Green 82), Craig Mahon; Akwasi Asante (George Waring 46), Anthony Dudley. Subs (not used): Matthew Thomson, Iwan Murray.
Boston (4-4-2): George Willis; Ben Davies, Ryan Qualter, Spencer Harris, Ashley Jackson; Max Wright (Jonathan Wafula 77), Nicky Wroe, Andi Thanoj, Nicky Walker (Brad Abbott 67); Gavin Allott (Andre Johnson 84), Jay Rollins. Subs (not used): Jordan Slew, Dylan Parkin (gk).
Referee: Matt Corlett.