The Pilgrims were 2-1 victors over Basford United at Greenwich Avenue to defeat their closest challengers from last season.
Bark opened the scoring in the second minute and after a Basford equaliser, Tate scored the winner with seven minutes to play.
Boston (4-2-3-1): Seth Greeves; Marshall Young, Taylor Gray, Peter Evison, Jack Brown; Jordan Tate, Jamie Gaukroger; Jenson Ball, Jenson Bark, Leighton Boughen; Ryan Pratt (Harrison Holland 75). Subs (not used): Jack Henton, Oliver Swaby (gk).