After a goalless first half, the match came to life after 58 minutes when Liam Moran handed the Pilgrims the lead.
Boston were unable to hang on though and Peterborough levelled in the 77th minute.
Boston (4-3-3): Jamie Bradley; Daniel Worthington, Daniel Moulds, Joe Cain, Jack McCallum; Miles Lynch, Liam Moran, Corey Newman (Jack Foyster 55); Scott Floyd, Louis Saebe, Steven Dovey (Conor Allen 55).