The Pilgrims had trailed 2-0 at Field Mill, but strikes from James Reed and Charley Sanders had hauled United back into contention.
However, the match referee's failure to award United a penalty when James Tricks' shot was handled in the box afforded Mansfield the chance to grab their 86th minute winner.
Mansfield roared into a two-goal lead through Clayton BROWN and Adam SOMES.
United responded either side of half-time with REED and SANDERS striking.
However, after Tricks had been denied a stonewall penalty and Mansfield's Ben Horsley had been handed his marching orders 11 minutes from time, the Stags won the contest through Scott ROGERS four minutes from the end.
Boston (4-4-2): Marc Hipwell; Niall Delahoy (Scott Langan 66), Lewis Sturman, Jordan Nuttell, Charlie Rossington; James Reed, Elliott Price, Jake Beauchamp, Jake Platten (Tom James 55); Charley Sanders, James Tricks. Sub (not used): Todd Devlin.