The Devils are 17-2-2 in their past 21 games. The Devils 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.
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 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.
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.
Notes: Florida F Rostislav Olesz has been placed on injured reserve because of a knee injury from Friday's game at Atlanta. ... F Chris Higgins broke his thumb in that game and will be out indefinitely. ... The Panthers recalled LW Kenndal McArdle and RW Hugh Jessiman from AHL Rochester. ... Ilya Kovalchuk had a 12-game points streak snapped.