Tlusty scored twice during Carolina's four-goal first, helping the Hurricanes take a 4-1 lead.
Carolina went up 2-0 when Ruutu scored from the low slot 3:27 into the game, and Tlusty added a rebound goal 1 minute, 14 seconds later.
After Thompson put home a backhand during a breakaway at 14:36 of the first, Harrison got the goal back just 34 seconds later.
Tlusty scored his second of the game to make it 4-1 at 16:18 of the first. A video review confirmed that Staal's pass, which deflected off Tlusty, entered the net before it became dislodged.
Purcell cut the Lightning deficit to 4-2 at 2:49 of the second. Carolina goalie Cam Ward stopped 17 of 18 shots during the period.
Carolina extended its advantage to 5-2 on Brent's goal at 13:41 of the third. Harrison assisted on the goal. Harrison also had a first-period fight against Ryan Malone.
Notes: Carolina C Jeff Skinner, who has missed 15 games because of a concussion, is practicing with the team and could return soon. ... The Lightning have been outscored 50-30 this season in the first period. ... Staal has seven assists and eight points during a four-game point streak. ... Tampa Bay D Eric Brewer played in his 800th NHL game. ... Carolina RW Chad LaRose sat out his second consecutive game due to an upper-body injury. ... The Panthers recalled D Derek Joslin from a conditioning assignment with Charlotte of the AHL.