Chris Wagner and Brad Marchand scored about five minutes apart in the second period for the Bruins, who lead the best-of-seven series 3-0.
Calvin de Haan scored for Carolina.
The Hurricanes, who entered the night with a 5-0 home record in the postseason, must win Game 4 at home on Thursday night in order to extend the series.
Carolina turned to goalie Curtis McElhinney for his first action of the series. He had filled in for injured Petr Mrazek for the final two-plus games of the second-round sweep of the New York Islanders.
McElhinny, who made 29 saves, was out the net for the final two minutes, but the Hurricanes couldn’t deliver a tying goal.
With 15:44 remaining the third period, Boston appeared to have increased the lead to 3-1 when the puck bounced off bodies and into the net. However, Boston’s Jake DeBrusk was called for goalie interference for making contact with McElhinney, wiping out the goal.
Wagner opened the scoring with a goal 1:21 into the second period, knocking in the puck from close to the crease.
Then Marchand produced his sixth goal of the postseason, this one coming on a power play at 6:28. The tally came with a fortunate redirection for the Bruins, with the puck hitting off the glove of de Haan and bouncing past McElhinney.
It was Boston’s third power-play chance of the game. The Bruins wound up 1-for-5 with the man advantage while the Hurricanes were 0-for-5.
De Haan got one back with his first career playoff goal later in the period.
The Hurricanes came out with a flurry, peppering Rask with shots. He stopped 19 shots in the first 18 minutes of the scoreless first period.
The period ended with Carolina holding a 20-6 edge in shots. That was the most shots in a period for the Hurricanes in a playoff game this year.
The Bruins reversed that in the second period by registering an 18-6 advantage in shots.
Carolina forward Saku Maenalanen was back in the lineup after missing four games due to a hand injury. He replaced Jordan Martinook, who is considered one of the team leaders but has labored with injuries during the postseason.
—Field Level Media