Worthington handed United an early lead and Squire struck when the Pilgrims trailed 3-1, before the Pilgrims eventually capitulated to lose 6-2.
To compound their woes, midfielder Jacob Pease was sent off for two yellow cards in the second half.
Boston (3-5-2): Jamie Bradley; Josh Spencer, Joe Cain, Ollie Price; Daniel Worthington (Harry Bunce 60), Miles Lynch (Corey Newman 65), Jacob Pease, Aaron Eyett, Bradley Easey; Liam Moran (Steven Dovey 70), Leon Squire.