The comeback started with 34 seconds left in the first, as Jordan Harmon lit the lamp on a pass from Mary Leech and Aggie Bisselle to make it 2-1.
In the second, Harmon doubled her tally on a pass from Bisselle to tie things up at 2-2, then the Bulldogs took the lead at the end of the second when Daisy Sullivan scored an unassisted effort to make it 3-2.
In the fourth, the Bulldogs got an insurance goal through Bisselle, with assists from Clara Berard and Mary Leech.
"We skated hard in the first, but it was not our best defensive effort," said BBA coach Ed Lewicki. "We really dominated the game in the second and third."
Lewicki gave his Player of the Game honor to Hartford goalie Erin Hudson, who stopped 51 shots for the Hurricanes. Hudson had 20 saves in the first period, 17 in the second and 14 in the third.
Kaylie Benson stopped 12 shots for BBA.
The Bulldogs improve to 8-1-1 with the win.
BBA girls basketball wins
WHITE RIVER JUNCTION -- In a game on Tuesday night, the Burr and Burton Academy girls basketball team topped Hartford 46-31 at Hartford.
Hartford led 20-18 at the break, but the Bulldogs came out in the second and outscored the Hurricanes 28-11 to take the win.
Hannah Nicholson led the Bulldogs with 11 points while Tessa Roberts added 10. Taylor Jackson had nine for Hartford.