Teravainen had two goals and an assist, Sebastian Aho, Andrei Svechnikov and Jordan Martinook each had two assists, and Curtis McElhinney made 34 saves for the Hurricanes (27-21-6) who won for the 12th time in the past 17 games (12-4-1) and the eighth straight time against the Sabres.
"I was pretty tired," Teravainen said. "I saw Justin Faulk there but then I saw he wasn't there anymore so I figured I'd go myself and try something. At the end, I felt like I should try a move and I got lucky, the goalie went for my move."
WATCH: [All Hurricanes vs. Sabres highlights]
Jeff Skinner scored twice, and Linus Ullmark made 24 saves for the Sabres (26-20-7), who lost for the fourth time in the past six games (2-3-1).
"It's a choice you got to make, protecting your own net, having a respect for it," Buffalo coach Phil Housley said. "You look at the game, the five of the six goals come right in front of our own net. That's the one thing players from our opposition should be very wary of going into. No. 1, we got to be tougher to play against. We've got to start pushing guys out, boxing guys out, have a fear that if something gets into that area, there's not going to be the looks that this team had tonight."