Alexander Semin scored 16 seconds into the game for the Hurricanes, who jumped ahead 3-0 and held on for their first victory against the Lightning this season.
Semin, who also had two assists, took a feed in the slot from Eric Staal and whipped it over the shoulder of Lightning goalie Andres Lindback. Eric Staal chipped in a pair of assists for Carolina.
Tlusty's first goal came shortly after the Hurricanes failed to score on a power play when he dumped the puck on goal from inside the blue line and it bounced off of Lindback's pads and into the back of the net.
Later in the period, Tlusty was stationed in front of the net and was in the perfect position to direct a deflection off of Staal's shot past Lindback.
The Lightning, who lost their sixth straight game, got on the board with a power-play goal from Steven Stamkos in the second period—his 28th goal of the season.
Martin St. Louis added a third-period goal to narrow the deficit to 3-2 but Ellis turned away the final 12 shots he faced, including point-blank opportunities by Eric Brewer, Ryan Malone and B.J. Crombeen.
With less than 20 seconds left, the Lightning pulled Lindback and created a lot of traffic in front of Ellis but could not tie the game.
NOTES: Staal thought he had a goal in the second period but the referee declared that his shot deflected off Brewer's skate but did not completely cross the goal line. ... St. Louis recorded his league-leading 42nd assist on Stamkos' goal. ... In their previous four contests this season, the Lightning outscored the Hurricanes 18-4.