The Pilgrims trailed Ilkeston FC 3-0 at the New Manor Ground before mounting a second half rally.
Lynch and Floyd struck on 58 and 77 minutes respectively, but the damage had been done by three early Ilkeston goals.
Boston (4-3-3): Jamie Bradley; Conor Allen (Joe Cain 55), Billy Hodgkiss, Daniel Moulds, Jack McCallum; Miles Lynch, Jack Dykes, Liam Moran; Steven Dovey, Karolis Andriulionis, Corey Newman (Scott Floyd 60).