The Hurricanes have earned a point in 12 straight games.
Andreas Athanasiou crashed into Eddie Lack as he scored in overtime Monday night
Cam Ward stopped 33 shots.
Joakim Nordstrom and Elias Lindholm scored for the Hurricanes, who have lost three of five.
Joakim Nordstrom also scored for the Hurricanes, and Cam Ward made 23 stops.
Carolina is tied with New Jersey for last place in the Metropolitan Division.
Tyler Johnson and Nikita Kucherov also scored to help the Lightning improve to 7-1-2 in the last 10 games.
Roberto Luongo stopped all three Carolina skaters in the shootout after making 23 saves.
The Hurricanes have lost six of seven to fall into last place in the Metropolitan Division.
Jordan Staal, Elias Lindholm and Viktor Stalberg scored for the Hurricanes.