Chara took a pass from Marc Savard behind the right circle and one-timed the puck past Cam Ward, sending the defending Stanley Cup champions to their fourth straight loss and third straight on home ice.
Glen Murray scored two goals, including his team-leading 26th, and Brad Boyes added a goal for the Bruins, who rallied from a 2-0 deficit with two goals in the second period.
Erik Cole scored two goals for Carolina and Rod Brind'Amour tied the game with 3:12 remaining in regulation. Tim Thomas made 34 saves for Boston, which for a while in the third period appeared to have halted its long losing streak.
Murray's second goal of the game put Boston up 3-2 with about 13 minutes to play.
But Brind'Amour tied it by scoring with a 5-on-3 advantage with 3:12 to play. He took a cross-ice feed from Ray Whitney on the right side of the goal and hammered it past a clearly agitated Thomas.
Cam Ward turned aside 29 shots for Carolina, which finally got some production from its power-play unit, scoring the game-tying goal with a two-man advantage and finishing 1-for-10 with the extra attacker. The Hurricanes entered the game 2-of-29 with the man advantage during their previous six games.
Cole got the Hurricanes' offence going early with two goals in the first period.
He put Carolina up 1-0 about four minutes into the game when he beat Thomas with a short wrist shot. He then extended the lead to two when he chipped a rebound high past Thomas for his first two-goal game since Jan. 6.
Murray pulled the Bruins to 2-1 with a power-play goal 30 seconds into the second when he tipped a rebound past Ward. Boyes tied it with 52.2 seconds left in the period when he shot out of the penalty box, took the puck on a breakaway and beat Ward with a wrist shot.
Notes: Murray has a five-game points streak. ... Carolina leads the season series 2-0. ... C Eric Belanger and defencemen Andrew Hutchinson and Anton Babchuk were scratched for Carolina. ... LW Marco Sturm and C David Krejci missed the game for Boston. ... The game was the nightcap of a basketball-hockey doubleheader at the RBC Center. Earlier in the day, North Carolina State upset No. 3 North Carolina 83-79.