Dwane Lee's second-half header earned Barnet three points against Boston.
Boston came out with all guns blazing, Lawrie Dudfield forcing goalkeeper Ross Flitney into action early on, but Barnet then began to get on top.
Ben Strevens saw an effort ruled out for handball before Lee headed the 47th-minute winner past Conrad Logan from Dean Sinclair's right-wing cross.
Nick Bailey saved the Bees when he cleared Jason Lee's mis-hit bicycle-kick off the line late on.
Barnet: Flitney, Batt, Charles, Yakubu, Clist, Lee, Sinclair, Bailey, Vernazza, Strevens (Norville 90), Hatch.
Subs Not Used: Tynan, Roache, Bowditch, Hickie.
Booked: Vernazza, Hatch, Bailey.
Goals: Lee 47.
Boston Utd: Logan, Canoville, McCann, Ellender, White (Lee 62), Holland, Rusk, Thomas (Maylett 82), Green, Joachim, Dudfield (Whelan 71).
Subs Not Used: Galbraith, Greaves.
Booked: White, Holland, Green, McCann, Lee.
Att: 2,287
Ref: J Moss (West Yorkshire).