Limb fired the Pilgrims into an early lead at Tattershall Road, only for Histon to score twice late in the first half to hold a 2-1 interval advantage.
Dykes grabbed a late equaliser for United, but Histon won it at the death with their third goal of the aftermoon.
Boston (4-3-3): Harry Payne; James Gordon, Kofi Ross, Daniel Moulds, Bailey Forth; Jack Dykes, Harry Vince, George Hobbins; Harry Limb, Kemal Yenibertiz, Scott Floyd. Subs (ALL used): Elliot Andrew, Oli Drummond, Jack McCallum, Tinashe Chavundura, Travis Portas.