Worthington and Moran accounted for Hitchin Town at RAF College Cranwell as the Pilgrims moved into round three.
Worthington handed the Pilgrims the lead four minutes before half-time, with Moran adding a goal just after the break and scoring his second and Boston's third nine minutes from time.
Boston (4-3-3): Jamie Bradley; Daniel Worthington, Billy Hodgkiss, Daniel Moulds (Jacob Pease 35), Jack McCallum; Miles Lynch, Liam Moran, Jack Dykes (Jack Foyster 55); Scott Floyd (Steven Dovey 60), Louis Saebe, Bradley Easey. Sub (not used): Connor Allen.