Nathan Gerbe had a highlight-worthy goal and Alexander Semin also scored for Carolina, which improved to 3-0 against Philadelphia this season.
Claude Giroux and Scott Hartnell scored for the Flyers, who lost for just the second time at home in their last 14 games.
Tlusty beat Flyers goalie Steve Mason from close range high to the glove side with 6:10 remaining.
The game originally was scheduled for Tuesday but was postponed due to the snowstorm that hit Philadelphia and much of the Northeast. As a result, Carolina also moved its home game against Ottawa from Friday to Saturday in order to avoid playing on three straight nights. The Hurricanes play at Buffalo on Thursday.
Semin opened the scoring for Carolina with just over 8 minutes left in the first period when he fired a wrist shot over Mason's glove hand into the top shelf.
Neither team generated much offense in the opening period, as the Hurricanes outshot Philadelphia 8-3.
Each team scored once in the second period, with Gerbe putting the Hurricanes up 2-0 with a breakaway goal with 6:22 left in the period. Gerbe benefited from a mistake by Flyers defenseman Luke Schenn, who misplayed a pass back to the point and couldn't recover when the speedy Gerbe got behind him.
He put the puck through his legs and wristed it past Mason with his hands in an awkward position on a goal that surely will be played countless times on the nightly highlight shows.
Philadelphia got on the board with 35 seconds left in the second when Giroux scored from a tough angle when his backhander ricocheted off the chest of Carolina goaltender Anton Khudobin and into the goal.
And the Flyers tied it just 3 minutes into the third period on Hartnell's power-play goal. Giroux took the initial shot from the top of the left circle and Wayne Simmonds failed on the rebound attempt. But the puck caromed off Khudobin and to Hartnell, who scored from point-blank range.
Mason had struggled in his last four games, with a 4.55 goals-against average, but brought a strong career record against Carolina into Wednesday's contest. Mason entered 5-1-1 with a 1.85 GAA against the Hurricanes. He finished with 29 saves.
NOTES: Tuesday's postponement marked the first time in Flyers history that a home game was postponed due to weather. Philadelphia had to postpone a home game on March 13, 1993, due to arena issues at the Spectrum. ... Philadelphia RW Jakub Voracek started after being questionable due to a left hand injury suffered in Monday's game against the Islanders. ... Carolina hadn't won three straight against Philadelphia since a six-game winning streak from Dec. 22, 1990-April 15, 1992 when they were the Hartford Whalers. ... Peter Laviolette was fired after Philadelphia's loss to Carolina on Oct. 6 and replaced by current Flyers coach Craig Berube. ... Carolina won for just the second time in the last 10 meetings against the Flyers in Philadelphia.
