Carolina won for just the second time in six games and handed the Lightning their fifth straight setback.
Tuomo Ruutu and Tlusty scored 1:14 apart early in the first period and then Jay Harrison and Tlusty tallied in the span of 68 seconds late in the stanza. They were the eighth and ninth goals of the season for Tlusty, whose career best for one season came in his rookie campaign of 2007-08 when he scored 10 for Toronto.
The win went to Cam Ward, who made 34 saves.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes