Substitute Jason Field scored United's only goal on an afternoon to forget for the Pilgrims.
United trailed 1-0 at half-time but imploded after the break to suffer their first away defeat of the campaign.
The Pilgrims were five goals down by the time FIELD, who had played 90 minutes the previous night for the reserves, gave United a small consolation.
United will be determined to bounce back ahead of next Wednesday's third and final FA Youth Cup qualifying round tie against Stourport Swifts at The Jakemans Stadium.
Boston (4-4-2): Marc Hipwell; Niall Delahoy, Lewis Sturman, Scott Langan (Jason Field 65), Todd Devlin; Joe Briers, Jake Beauchamp, Luke Wilson, Jake Platten (Jonny Butler 65); Jordan Nuttell, James Tricks. Sub (not used): Charley Sanders.