Ondrej Palat supplied a goal and two assists as the Lightning rebounded from a 5-4 loss to San Jose Saturday.
Nikita Kucherov and Teddy Purcell also scored for the Bolts.
Eric Staal notched a goal and an assist for the Hurricanes, losers of three of their last four games.
Justin Peters started in net for Carolina but was lifted in the first period after letting in three goals on Tampa Bay's first seven shots.
Anton Khudobin turned aside 13-of-15 tries the rest of the way.