The Hurricanes entered the game 31st on the penalty kill on the road.
"We've got to win the special teams battle though, we've been struggling on the kill," Carolina defenseman Jaccob Slavin said. "The guys...we played hard, we've just got to be more consistent. We know our structure works. We just have to do it better."
Barre-Boulet extended it to 2-0 at 17:51 of the second period. He swept the puck from behind the net to Darren Raddysh outside the right circle, and Raddysh’s slap shot was tipped in by Barre-Boulet.
"He's got some gifted offensive talents," Cooper said of Barre-Boulet. "So, we just have to put him in a situation to succeed. He's making the best of his opportunity. I'm really happy for him."
Nicholas Paul made it 3-0 at 17:04 of the third period with a one-timer from the left circle that beat Kochetkov to the far post.
"Everyone battled out there, but at the same time, it doesn't matter what the effort is if we scored zero goals," said Carolina center Sebastian Aho, who returned after missing three games with an upper-body injury. "Every game we have enough chances to win a hockey game. It's a matter of putting the puck in the net."
NOTES: Aho was minus-1 with three shots on goal in 21:05 of ice time in his return. ... Lightning captain Steven Stamkos did not have a shot on goal for the second straight game (one shot attempt). ... Hurricanes defenseman Brent Burns was minus-2 and played his 767th consecutive game, the ninth-longest streak in NHL history (Craig Ramsay is eighth with 776).