The sides shared a 4-4 draw across 60 minutes - before a further hour saw the Posh prevail 2-0, with David Kamara on target twice.
Earlier on, Kwame Poku and Ricky-Jade Jones had fired the visitors into a 2-0 lead inside nine minutes, with Dan Mooney soon on target for the Pilgrims. Tony Weston and Chris Conn-Clarke both added braces for their respective sides, with Cameron Green scoring a brilliant, long-range equaliser.
United (first 60): Cameron Gregory, Cameron Green, Michael Bostwick, Tom Leak, Jacob Hazel, Dan Mooney, Tony Weston, Jordan Richards, Sam Osborne, Frankie Maguire, Jacob Scott.
United (second 60): Jake Lovelace, Mitch Roberts, Keaton Ward, Martin Woods, Adam Marriott, Jai Rowe, Pemi Aderoju, Zak Mills, Dylan Hill, Josh Doran (Ed Daffern 50), Trialist D (Finley Ging 52).
Referee: Aaron Bannister.
Attendance: 1,248 (466 visitors).
PIC: Russell Dossett.