The Pilgrims were 1-0 victors over Peterborough United at Manor School Sports College to extend their unbeaten league sequence to five matches.
Newman struck the decisive goal on 65 minutes — and United kept a clean sheet to seal three valuable points.
Boston (4-3-3): Jamie Bradley; Daniel Worthington, Daniel Moulds, Joe Cain (Conor Allen 72), Jack Foyster; Miles Lynch, Liam Moran (Karolis Andriulionis 77), Corey Newman (Jack McCallum 72); Steven Dovey, Louis Saebe, Scott Floyd.