Carl Soderberg assisted on both goals for Boston, which held off the Jets during a four-minute power play late in the third period and early in overtime. Hamilton's high wrist shot over goalie Michael Hutchinson's glove ended it.
Loui Eriksson also earned an assist on the game-winner. Boston's Milan Lucic scored the tying goal early in the third period, and Tuukka Rask made 35 saves. He didn't allow anything to get past him after Dustin Byfuglien's goal gave the Jets a 1-0 lead with 3:36 left in the first period.
Hutchinson stopped 36 shots, including a flurry of late chances for Boston that followed mistakes by the Jets.
Boston had the better opportunities following Brad Marchand's double-minor penalty with 3:30 left in the third when his stick clipped Grant Clitsome in the head behind the Jets' net. Boston almost converted it into a short-handed goal with 30 seconds remaining in regulation.
Daniel Paille stole the puck from Hutchinson and passed it toward Campbell in the slot, but Hutchinson recovered with a glove save. The Bruins also missed on a pair of rebounds early in overtime.
Boston tied it at 1-1 on Lucic's goal 3:05 into the third on a give-and-go with Carl Soderberg, whose pass back to Lucic in front of the net set up an easy backhanded tip. Hamilton also got an assist on the goal,
It was Boston's first goal since Lucic and Joe Morrow scored 28 seconds apart early in the second period of a 3-2 overtime loss to Pittsburgh on Monday night.