Sebastian Aho had two goals and an assist, Andrei Svechnikov scored for a third straight game, and Frederik Andersen made 27 saves for Carolina (3-0-0).
Kotkaniemi, who was booed every time he touched the puck, got his first point in three games for the Hurricanes.
"It felt really good," Kotkaniemi said. "It was a big relief after those first two games. But it was a great feeling to get it over here too."
It was Kotkaniemi's first time facing the Canadiens since they announced Sept. 4 that they would not match the one-year, $6,100,015 offer sheet the Hurricanes tendered to the restricted free agent forward. The 21-year-old played three seasons for Montreal, which selected him No. 3 in the 2018 NHL Draft.
"That's tough for anybody new, whether you're a young kid or not, you don't want to hear that," Hurricanes coach Rod Brind'Amour said. "But I think he expected that kind of reaction, it's just the way it is. So he answered that the best way he could."