Given another opportunity against the team that embarrassed them the night before, the Hurricanes used two goals from Staal en route to a 3-2 win over the Panthers on Saturday.
"It was a better effort from everybody, including myself," Staal said. "I wasn't happy with the way I played last night. It wasn't a very good feeling in our locker room last night and it wasn't a very good feeling on the flight home.
"We wanted to respond the right way and we did."
Jeff Skinner also had a goal and an assist, and Cam Ward made 18 saves for the Hurricanes, who were beaten 7-4 at Florida on Friday.
Darcy Hordichuk and Michael Frolik scored for the Panthers, and Scott Clemmensen made 26 saves.
Both teams found offense harder to come by on the back end of the home-and-home series. After consecutive 50-shot efforts, Florida had only nine through two periods Saturday as Carolina clamped down.
"It was just about work ethic and execution," Carolina forward Erik Cole said. "Last night we didn't have it. Tonight, we did. We brought a much tougher game to play against, and I think it showed."
After a first period with few scoring chances, Staal took a pass from Sergei Samsonov in the slot and one-timed a shot past Clemmensen's glove while the Hurricanes had a 5-on-3 power play midway through the second. The Hurricanes squandered a prolonged two-man advantage in the third period of Friday's loss.
"Even if we hadn't scored on that 5-on-3, at least you could live with it because you made the goaltender make a bunch of saves," Carolina coach Paul Maurice said. "I'm glad they scored because they deserved it."
Carolina built its lead early in the third period when Cole skated around the net and backhanded a perfect pass to Skinner, who knocked the puck past Clemmensen while parked in the crease.
Skinner entered the game leading NHL rookies with 10 points.
Florida responded one minute after Skinner's goal when Hordichuk beat Ward from just outside the crease.
"They're a fast team. They showed that," Florida forward David Booth said. "On the other end, we weren't good enough. If we would've played the game last night, I think we would've been all right."
Staal gave the Hurricanes another two-goal lead when he skated over the blue line on a rush and snapped a wrist shot that deflected off a Florida defender and through Clemmensen, who was off-balance.
Frolik brought the Panthers within 3-2 with 42.2 seconds remaining when he surprised Ward with a wrist shot from the boards near the circle.
"We were in it, for the most part. All game long, we were right there," Clemmensen said. "So nothing to hang our head about, but it's disappointing not to get the win. It always is."
The Hurricanes have won 17 of 19 home games against the Panthers and are 25-5-2 overall while facing the Panthers at the RBC Center.
Carolina had scored a combined 11 goals in its previous two games.
Carolina D Joni Pitkanen missed his second straight game because of an upper body injury. Florida LW Cory Stillman sat out after injuring a shoulder Friday. Carolina D Joe Corvo played in his 500th NHL game.