Patrice Bergeron scored, and Ullmark made 20 saves for Boston (22-12-2), which had won five in a row.
"It's problematic against anybody," Bruins coach Bruce Cassidy said. "We're building our game, and have been playing well lately, much better than the start of the year, but obviously not tonight. We had nothing. They were clearly better than us in every area. … We didn't compete."
Teuvo Teravainen gave Carolina a 1-0 lead at 3:44 of the first period with a one-timer from the right face-off circle. Kotkaniemi made it 2-0 at 6:03 on a rebound in front after Rask made a save on Andrei Svechnikov.
Bergeron cut it to 2-1 on the power play at 11:13 when David Pastrnak's pass deflected off his skate and through Andersen's legs, ending Carolina's streak of 35 straight penalties killed.
Kotkaniemi scored his second of the game 13 seconds later to make it 3-1 at 11:26, redirecting Slavin's slap shot from the point.
Seth Jarvis made it 4-1 at 16:01 on a drive to the net following a Bruins turnover in the neutral zone, and Derek Stepan pushed the lead to 5-1 56 seconds later, scoring off a no-look pass from Jordan Martinook at 16:57.
"Our mindset coming into the game was in the right spot from the beginning," Stepan said. "This was one of the good games that right from the start, we did a lot of the things we wanted to. That's what you need on a consistent basis. Nothing changes going into the next one."
Slavin made it 6-1 on the power play at 3:05 of the third, and Svechnikov's power-play goal made it 7-1 at 7:48.
NOTES: Carolina last allowed a power-play goal Dec. 7 in a 4-2 win against the Winnipeg Jets. … It was Slavin's sixth NHL game with at least three points. Three defensemen in Hurricanes/Hartford Whalers history had more: Dave Babych (12), Mark Howe (12) and Zarley Zalapski (seven). … Slavin and DeAngelo became the sixth pair of Hurricanes/Whalers defensemen to score at least three points in the same game. The others were Dougie Hamilton and Slavin (Nov. 1, 2019, against the Detroit Red Wings); Dennis Seidenberg and Anton Babchuk (April 7, 2009, against the New York Islanders); Glen Wesley and Sean Hill (Nov. 23, 2002, against the Montreal Canadiens); Kevin Hatcher & Sandis Ozolinsh (March 4, 2001, against the Chicago Blackhawks), and Dave Babych and Brad Shaw (Oct. 26, 1989, against the New Jersey Devils). … Carolina scored at least six goals in a game for the seventh time this season, trailing only the Colorado Avalanche (nine). … Rask made 25 saves in his season debut Thursday, a 3-2 win against the Philadelphia Flyers. … The Bruins
retired Willie O'Ree's No. 22
before the game. Tuesday was the 64th anniversary of the Hockey Hall of Famer becoming the first Black player in the NHL when he debuted for Boston against the Canadiens at the Montreal Forum. O'Ree played both of his NHL seasons for the Bruins (1957-58, 1960-61).