Drew Larman, Nathan Horton, Jay Bouwmeester and former Ducks defenseman Ruslan Salei scored for the Panthers, who rallied to tie after trailing 4-2 in the third period.
"We knew we were playing a good team," Bouwmeester said. "They found a way to get it done, and good teams often do that. They work hard and worked for what they got."
Jean-Sebastien Giguere made 27 saves for Anaheim. Alex Auld stopped 31 shots for the Panthers.
Giguere made his best saves in the final minutes after Pronger gave Anaheim the lead for good.
"Yeah, he made some stops," Anaheim coach Randy Carlyle said, "but that's what goalies are supposed to do."
Pronger scored the deciding goal after Anaheim won a faceoff in the Florida zone. Pronger's shot went through a crowd and beat Auld low to the stick side with nine minutes left.
"I was just shooting blocker side," Pronger said.
Pronger's first goal, at 3:34 of the third period, gave the Ducks a 4-2 lead. He scored on the power play when he beat Auld with a one-timer from the point.
"The (shots) found a way to get through," Carlyle said. "Some big-time shots from a guy who can shoot the puck really hard."
Bouwmeester cut the deficit to 4-3 at 4:56 with a slap shot from just inside the blue line that got past Giguere's glove.
Salei, in his first game against the Ducks following nine seasons with them, then took a pass from Olli Jokinen and beat Giguere from the slot.
Anaheim outshot Florida 14-6 in the first period and ended up with a 36-31 advantage.
"We had a good start, a good first period," Carlyle said. "In the end we were hanging on, it's as simple as that."