After a goalless first half at Boston Town’s DWB Stadium, the Pilgrims took the lead through Floyd’s penalty.
Peterborough subsequently levelled — but Andrew emerged from the bench to score a late winner for the hosts.
Boston (4-4-2): Harry Payne (Travis Portas 46); James Gordon (Oli Drummond 55), Kofi Ross, Daniel Moulds, Bailey Forth; Jack McCallum, Jack Dykes, Harry Vince, Scott Floyd; George Hobbins (Elliot Andrew 70); Tinashe Chavundura. Subs (not used): Jordan Tate, Peter Evison.