The home team won each game of the best-of-7 series.
Carolina will play either the New York Rangers or Pittsburgh Penguins in the second round. Game 7 of that series is at New York on Sunday (7 p.m. ET; TBS, SN360, SNE, SNO, SNP, MSG, ATTSN-PT).
Teuvo Teravainen had a goal and an assist, and Antti Raanta made 27 saves for the Hurricanes, the No. 1 seed in the Metropolitan Division. Jaccob Slavin had two assists.
"Our top guys played really noticeably well," Carolina coach Rod Brind'Amour said. "It was the right way. Everything was right, from the start to the last 20 seconds when it got a little hairy. A solid, solid game."
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Jake DeBrusk and David Pastrnak scored, and Jeremy Swayman made 28 saves for the Bruins, the first wild card from the East. Charlie McAvoy had two assists.
"We ended up having some breakdowns," Boston coach Bruce Cassidy said. "We pride ourselves in D-zone coverage, stuff we've done really well all year. Yeah, they make plays, but [it's] more on us to get the job done defensively. That's probably where I'm most disappointed that's how it ends up."
Taylor Hall had Boston's best scoring chance at 10:39 of the first period after he took a pass from Erik Haula on a 2-on-1, but Raanta made a sprawling right-pad save to keep the game 0-0.
"If we bury that 2-on-1, things might change in a game like today when it's hard to score," Cassidy said. "If you get the lead, [it's] a little adversity on their part."
Raanta, who took over the No. 1 role after Frederik Andersen sustained a lower-body injury against the Colorado Avalanche on April 16, was 3-2 with a 2.37 goals-against average and .927 save percentage in six starts in the series.
"When one of the best goalies in the League goes down with an injury, obviously it's going to sting a little bit, but like we've been playing the whole year, the team in front of me is doing a great job," Raanta said. "I just tried to do my job and help the guys to get the win."