RALEIGH, N.C. -- The Tampa Bay Lightning weren't about to let themselves fall behind on the road again.
Ryan Malone added a power-play goal, and Vincent Lecavalier assisted on both early scores for the Lightning, who were still fuming about how they dropped into a four-goal hole on Monday in a 4-3 loss to the New York Islanders.
The Lightning -- who were 13-22-6 in road games last season -- scored twice in the first period to set the tone. They pulled away with two more in the third period and continually clamped down on a Carolina offense that added Jordan Staal and Alexander Semin during the offseason.
"We were (ticked) off about (Monday's) game. We weren't playing the way we wanted to," Pyatt said. "We played better defensively. We were all above them, we took their space away, and I think it got them frustrated."
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.
"There's no panic, but we've definitely got to find a way to work harder and find a way to win games," Staal said.
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.
"We wore down the opponent to get to the third period, and then our offense came out because we were doing a good job defensively" in a season-opening 6-3 win over Washington, Lightning coach Guy Boucher said. "We made the mistake of doing the opposite (Monday). Today, we wanted to make sure we came back to that.
"Slowly, that's how we want to wear teams down," he added. "We know we've got the offense. We know we can punch on any moment, but we don't want to force it."
Ward was back in net three nights after allowing four goals on just 12 shots in a 5-1 loss at Florida. The Lightning continued his rough start by scoring on two of their first five attempts.
Pyatt struck first 5:18 in when he got past Bobby Sanguinetti, took a pass from Lecavalier, and batted the puck out of the air past Ward.
"I saw it coming. Obviously, there was a little bit of luck in there, too," Pyatt said. "I never played any baseball or anything, but I guess it came natural."
Conacher made it 2-0 by shoving in a rebound with 8:24 left.
"There's some good things in our game, but there's a little bit where I think we just need to get down and get gritty, compete a little bit more on pucks and one-on-one battles, and being physical in the corners and make it difficult for teams to get to our net," Carolina captain Eric Staal said. "Clean that up, and we'll be fine. We had enough offense. We had some good looks, and just didn't capitalize enough."
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. . 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.