Vince's first half penalty and Stocks' second half strike sealed three points for Martyn Bunce's side in a 2-0 win.
The only downside for United was a potentially serious ankle injury sustained by midfielder Oli Drummond.
Boston (4-3-3): Harry Payne; James Gordon (Oli Drummond 46), Jack Withers, Bailey Forth, Callum Rodger; Jordan Tate, Harry Vince, Peter Evison; Ben Lawrence (Jenson Ball 46), George Smith (Connor Stocks 46), Jack Brown.