United's trip to Leicestershire resulted in a rare 0-0 scoreline for the Pilgrims' youngsters.
Boston carried the greater threat throughout but were unable to find a crucial breakthrough and were forced to play most of the second half with 10 men following an injury to Bradley Easey.
Boston (4-3-3): Jamie Bradley; Daniel Worthington, Billy Hodgkiss, Daniel Moulds, Jack McCallum; Miles Lynch, Liam Moran, Jack Dykes; Scott Floyd, Conor Allen (Jack Foyster 46), Bradley Easey.