The Pilgrims overturned a one-goal deficit to defeat Peterborough United 2-1 at Manor College in Raunds.
Floyd struck the equaliser after 80 minutes and Chavundura swooped to score the winner in stoppage time.
Boston (3-5-2): Harry Payne; James Gordon, Daniel Moulds, Elliot Andrew; Jack McCallum (Scott Floyd 50), Jack Dykes, Harry Vince, Oli Drummond, Bailey Forth; Kemal Yenibertiz, Tinashe Chavundura. Sub (not used): Liam Mead.