Clemmensen, playing against his former teammates, made nine stops on nine first-period shots.
Frolik scored in the second and third periods.
Frolik's 8th goal (power play) this season gave Florida a 2-0 lead at the 2:24 mark of the second, and the Devils never led.
New Jersey got one goal each from Brian Rolston and Dean McAmmond.
Net-minder Martin Brodeur was beaten four times on 22 shots for the Devils, who had won four in a row and seven of eight.
Brodeur was trying to pass Hall of Famer Terry Sawchuck's record 103 career shutouts.