Carolina has allowed four or more goals in 10 of its last 14.
The Hurricanes dominated play in the early minutes, outshooting Boston 7-0.
"We were under a lot of pressure handling the puck in our own zone," Seidenberg said.
Rask stopped a handful of close shots, including a left pad stop of Zac Dalpe, who was alone at the edge of the crease.
"We've got to find a way to dig deeper," Bowman said. "It's very frustrating. It's happened each of the last three games. We've got to come out and keep fighting; eventually we'll get the first goal."
After the poor start, the Bruins jumped ahead 1-0 when Peverley fired a shot from the right wing, collected his own rebound at the edge of the crease, circled the net and tucked a shot past goaltender Justin Peters inside the left post.
Just over 5 minutes later, Boston's new second line of Marchand-Gregory Campbell-Jaromir Jagr made it 2-0. Marchand banged in the rebound of Campbell's shot from the edge of the crease.
"We definitely played well tonight," Marchand said of his new line. "We only had one practice together."
The Hurricanes replaced Peters with Dan Ellis after the second goal. Peters faced only four shots in 7 minutes, 58 seconds.
The Bruins made it 3-0 when Jagr tried a wraparound shot. Ellis made the save, but the puck caromed out to Marchand, who backhanded a shot in from the bottom of the left circle for his team-leading 16th goal.
Boston increased it to 4-0 on Ference's score early in the second. Seidenberg fired a shot from the left point, the puck popped in the air and into the net off Ference's left glove. After a reply review, the call on the ice was upheld.
Caron's score made it 5-0 midway into the second, but the Hurricanes ended Rask's shutout bid when Dwyer scored on a rebound midway into the third.
Bowman's goal cut it to 5-2 before Horton redirected Dougie Hamilton's pass for his 13th of the season.
"It's nice, but it doesn't really matter in a loss," Bowman said.
Julien dropped Tyler Seguin from the second line to the third, moving Campbell up to center the second. ... Boston improved to 8-0-1 in its last nine home games. ... Bruins C Patrice Bergeron missed his second straight with what the team called a "moderate" concussion. ... The Hurricanes entered equally as bad with the power play or short-handed, ranking 28th overall. ... Boston C Chris Kelly returned after missing 14 games with a broken bone in his left leg. ... It was the first of four of six on the road for Carolina.
Copyright by STATS LLC and The Associated Press
BOSTON, MA - APRIL 8: Jeff Skinner #53 of the Carolina Hurricanes is interviewed during warm ups before the game...