In a meeting of division leaders, the Hurricanes ran off four goals in a row to hand Marc-Andre Fleury his first loss in six appearances.
Chris Kunitz scored for Pittsburgh with 6:46 to go in the first period, but Ward was perfect the rest of the way while stopping 26 shots.
Eric Staal tied it just 25 seconds from the first intermission and Tlusty gave Carolina the lead 4:03 into the second on a slap shot.
Jeff Skinner recorded his eighth goal of the season less than 2 minutes later and Tlusty tallied again 21 seconds from the end of regulation.
The four Carolina goals came on 29 shots.
Carolina went into Thursday's games as the only winning team in the Southeast Division.