With the game tied 2-2 at the 7:25 mark of the final period, the Hurricanes were on a power play when Eric Staal got control of the puck behind the net and found Tlusty to the left of the goal.
Tlusty clinched the game with an empty-net score while Jussi Jokinen and Patrick Dwyer also tallied for the Southeast Division-leading Hurricanes, who improved to 5-1-1 in February.
Cam Ward made 26 saves in the victory.
lya Kovalchuk and Ryan Carter scored while Brodeur finished with 21 saves for the Devils, who were handed just their second regulation defeat.
Celebrity Families of 2014 [PHOTOS]