"This team has been a problem for us," Whitney said. "I think patience was what won it for us. We didn't force too many things."
Tampa Bay had won 13 of the previous 20 games between the teams.
Whitney gave Carolina a 2-1 lead with a goal from the left circle during a delayed penalty call at 9:31 of the third. The left winger, who has a three-game goal streak, added an empty-netter with one minute left.
Whitney passed up a chance for his third goal when he set up Staal's late goal.
"For me, it doesn't matter," Whitney said. "Staal, I thought he played an unbelievable game."
"You've got a kid, who's playing [strong] in net, you've got young defensemen who are getting run all over the place by a quick Carolina team. I'm disappointed in the core," Tampa Bay coach John Tortorella said. "I didn't like anything about our third period. That falls on the core. No one else. I'm totally disgusted as far as what happened there."
The Lightning have scored two goals or less in seven of nine games. Tampa Bay had four shots, but failed to score during a long 5-on-3 power play in the second.
"It always does change momentum," Hurricane left wing Cory Stillman said. "If you don't score 5-on-3, it ends usually costing you a hockey game, especially in a tied game or even if you're up by one."
St. Louis put the Lightning up 1-0 just 23 seconds in. Ward stopped St. Louis' shot from the left circle, but the rebound hit Hurricanes defenseman Glen Wesley in the back and trickled into the net.
Wesley nearly tied it midway through the first, but his shot hit the crossbar. The Hurricanes pulled even at 1 when Ladd scored a rebound goal with 1:56 left in the period.
Tampa Bay had a goal disallowed after a video replay with 1:09 left in the second. The replay showed that Mathieu Darche used a kicking motion to put a rebound of Vincent Lecavalier's shot into the net.
The Hurricanes almost grabbed a one-goal advantage in the final seconds of the second, but Erik Cole hit the post on his rebound try.
Carolina center Brandon Nolan, the son of New York Islanders coach Ted Nolan, had an assist in his NHL debut. The Hurricanes said Nolan is the 15th son in league history to play a game in the same season that his father served as a head coach.
"I tried to get some quick updates in-between periods, and when I heard he got an assist I was real proud of him, just like how any father would be," Ted Nolan said after the Islanders' home victory over Washington. "He's spent a few years in the minors and earned his chance to play in the NHL, and I'm glad he's making the most of his opportunity."
Wesley played in his 1,416 NHL game, moving him into a seventh-place among defensemen with Hall of Famer Al MacInnis. ... Tampa Bay C Craig MacDonald didn't play, two days after being struck in the month by a shot taken by Toronto's Hal Gill. MacDonald broke nine teeth and needed over 50 stitches for cuts on his tongue and inside his mouth. ... Hurricanes RW Craig Adams served the second and final game of a suspension for a high-sticking incident last Tuesday. ... Carolina D Mike Commodore sat out with a left foot injury. ... Tampa Bay C Chris Gratton (hip) returned after missing three games.