Steven Stamkos, Ondrej Palat and Victor Hedman each had a goal and an assist, and Andrei Vasilevskiy made 34 saves for the Lightning (11-4-1), who were coming off a 4-0 loss to the Hurricanes on Saturday.
"We blocked a ton of shots (15), and when we didn't, [Vasilevsky] was there," Tampa Bay coach Jon Cooper said. "When you play good teams, you're going to get leaned on. I like the fact that we didn't break."
Jesper Fast scored his first two goals with the Hurricanes (12-4-1), who were 5-0-1 during their streak. James Reimer made 28 saves.
"We were a little off at the start, but we built a game after that," Carolina coach Rod Brind'Amour said. "But they were the better team overall, and that's why they got the two points."