The Devils are 17-2-2 in their past 21 games. They climbed within nine points of eighth-place Carolina in the Eastern Conference, while the Panthers remained eight points back of the postseason cutoff.
Brodeur hadn't played since injuring his right knee on Feb. 6 in Montreal.
"The guys played really well in front of me and that's nice when you haven't played in a long time," Brodeur said. "Everything (with the knee) was OK. It's kind of nice to test it in a game."
Marty Reasoner scored for Florida and Tomas Vokoun made 24 saves.
The Devils took a 1-0 lead at 5:46 of the second period. Rod Pelley took a shot from the slot and Vokoun blocked it. The puck bounced out to the left corner of the crease and Clarkson swept in a backhand shot past Vokoun for his ninth goal of the season.
"The puck hasn't been going in for me (lately), but I'm getting chances and I'm trying to go around the net and create chances," Clarkson said.
The Devils stretched their lead to 2-0 a few minutes later on Rolston's power-play goal. The Devils won the faceoff and Dainius Zubrus pushed the puck out to Rolston above the left circle. His slap shot went through Vokoun's pads at 9:11.
"Their primary guy got kicked out, and I was thinking if I got it clean I would try to get a good shot off," Rolston said. "That one kind of snuck through, but I was fortunate enough get it."
Three of the four games between the Panthers and the Devils this season were decided by one goal.
"It's always a one-goal game," Rolston said. "Except for that one in New Jersey, they're one-goal games and it's tough to get opportunities, but the power play was the difference tonight and it was good to get one."
The Devils are hoping to make a late push for the playoffs and coach Jacques Lemaire is pleased with the effort.
"The guys were not playing together. Now they feel better about each other and they're helping each other on the ice," Lemaire said.
The Panthers lost for the fifth time in seven games.
"They're the hottest team in the NHL right now," said Florida's Dmitry Kulikov, who returned after missing seven games with an ankle injury. "We put up a good effort against them. We just didn't get our bounces."
Reasoner's goal came at 15:31 of the third. Michal Repik brought the puck out from behind the net to Reasoner at the left corner of the crease. His shot beat Brodeur. It is the first time this season that Reasoner notched goals in consecutive games.
The Panthers played with four players called up from the AHL since last Thursday, including two who arrived on Sunday. Hugh Jessiman was part of that group and became the 30th player drafted in the first round of the 2003 Entry Draft to appear in an NHL game.
"The guys emptied the tanks and gave us what they had," Panthers coach Pete DeBoer said, "but it's not enough."
Material from wire services and team media was used in this report.