Bergeron scored his first goal at 11:50 of the first period, and the Bruins broke the game open with goals by Carl Soderberg and Bergeron in a 13-second span early in the third.
Tuukka Rask stopped 28 shots in posting his NHL-leading seventh shutout.
Chicago, fourth in the Western Conference, remained one point short of clinching a playoff berth for the sixth straight season.
The Eastern Conference-leading Bruins rebounded from a 2-1 shootout loss to the Montreal Canadiens on Monday that ended Boston’s 12-game winning streak. In their last 14 games, the Bruins have outscored opponents 51-19.
The Blackhawks, the NHL’s highest-scoring team, played without Patrick Kane, the Conn Smythe Trophy winner last season as the postseason MVP. Chicago’s second leading scorer is expected to miss the rest of the regular season because of a knee injury.
In Game 6 of the Stanley Cup finals, the Bruins allowed two goals in the last 76 seconds as the Blackhawks clinched their second championship in four seasons with a 3-2 victory. Brian Bickell tied it with 1:16 to play and Dave Bolland scored the winner with 59 seconds left.
But on Thursday, the Blackhawks had few good scoring opportunities. Their last solid bid came when Jeremy Morin unleashed a hard, 30-foot shot from the left side that a sprawling Rask plucked out of the air with his glove.
Bergeron began the scoring when he tipped in Matt Bartkowski’s shot from the left point as the puck eluded goalie Corey Crawford.
Soderberg made it 2-0 with his 14th of the season at 5:28 of the third period. Johnny Boychuk’s shot was stopped by Bruins forward Chris Kelly in front, and it went to Soderberg, who shot quickly from 15 feet.
Just 13 seconds later, Bergeron was credited with his 25th goal after a video review. Crawford had gone behind his net, and when he tried to get back in front, he knocked the net out of position as the puck was heading toward it. Officials ruled that the puck would have gone into the net had it been in place.
NOTES: A moment of silence was held before the game for firefighters, Lt. Edward J. Walsh and Michael R. Kennedy, who died Wednesday in a fire in the Back Bay section of Boston — not far from TD Garden. … Bergeron has a career-best, five-game goal streak. … The Bruins are 6-0 when they take a 1-0 lead into the third period.
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