Tom Pyatt and Cory Conacher scored early goals, Ryan Malone added a power-play tally, and Vincent Lecavalier had two assists. The Lightning pulled away with two goals in the third period.
Jeff Skinner scored a power play goal for the Hurricanes, who had their home opener spoiled by Tampa Bay for the second straight season.
Mathieu Garon stopped 35 shots—including all 15 he faced in the third period of his first start this season for the Lightning, who opened the lockout-compressed season with two wins in three games.
Cam Ward made 22 saves, but allowed four goals for the second straight game. The Hurricanes have started a much-anticipated season with two losses and have been outscored by a combined 9-2. Carolina has dropped four straight home openers.
Skinner cut Carolina's deficit to 2-1 when he scored a power-play goal 3:45 into the second, backhanding a rebound high past Garon.
Aulie restored the Lightning's two-goal lead 1:37 into the third when he skated unimpeded into the left circle and beat Ward with a high shot for his first goal since the 2010-11 season.
Malone then put Tampa Bay up by three when he stuffed in a loose puck on the power play with 10:03 left.
Ward was back in net three nights after allowing four goals on just 12 shots in a 5-1 loss at Florida—and the Lightning continued his rough start by scoring on two of their first five attempts.
Pyatt struck first just 5:18 in when he got past Bobby Sanguinetti, took a pass from Lecavalier and batted the puck out of the air past Ward. Conacher made it 2-0 by shoving in a rebound with 8:24 left.
Notes: The Sanguinetti-Joni Pitkanen defensive pairing for Carolina was on the ice for Tampa Bay's first two goals. . Conacher has five points in three games. . Carolina's Alexander Semin struck the left post with a shot during a power play early in the second period. . Former Pittsburgh Steelers coach Bill Cowher watched from the stands. His son-in-law, RW Kevin Westgarth, made his debut with Carolina.