David Savard, Boone Jenner and Tyler Motte scored for the Blue Jackets, and Markus Nutivaara had two assists. Savard gave them a 1-0 lead at 1:59 of the first, taking a pass off the wall from Alex Wennberg.
Jenner, who missed the first seven games with a middle-body injury, made it 2-0 with 2:52 left in the first period.
Motte, playing in place of the injured Cam Atkinson (lower body), scored in his first game with Columbus for a 3-0 lead at 8:27 of the second period. He took a stretch pass from Nutivaara at the blue line, skated in and shot five-hole on Rask for his fifth NHL goal.
"It was a great pass," Motte said. "I'd like to see how far it traveled before it reached my stick."
Motte was acquired by Columbus on June 23 with Panarin in a trade that sent Brandon Saad to the Chicago Blackhawks.
Tortorella said Boston's comeback started when Brandon Dubinsky was called for tripping at 14:59 of the second to give the Bruins a power play after the Blue Jackets had them pinned in their own end for more than two minutes.
"Bad penalty. Bad timing," Tortorella said. "That's a tired team on the ice. They iced the puck and they have to stay on the ice. We don't move our legs. You just know you're not going to kill it off. We weren't the same after that."
Bergeron scored a power-play goal at 15:37 of the second period to make it 3-1 and end the Blue Jackets streak of 16 straight penalty kills.
"We have a lot of character in our room and we recognized that wasn't the way we wanted to play," Rask said. "We battled back and still found a way to get a point. That's a big point."
