The trio were on target at the New Manor Ground as the Pilgrims defeated Ilkeston FC 3-2.
Forth and Vince had fired United into control before Ilkeston levelled — only for Tate’s 75th minute strike to seal all three points.
Boston (4-3-3): Harry Payne; James Gordon, Jack Withers, Bailey Forth, Jack Brown; Peter Evison (Oli Drummond 55), Harry Vince, Jordan Tate; Liam Adams, George Hobbins, Haydn Havard (Jenson Ball 70). Sub (not used): Connor Stocks.