Clarkson scored the decisive goal on a tip-in at 10:43 of the third period to seal the comeback after the Devils trailed 3-1 after the first period. Patrick Elias scored the game-tying goal and also had two assists for the Devils.
Ilya Kovalchuk notched three assists.
Travis Zajac gave the Devils a 1-0 lead with a goal 40 seconds into the first period.
Martin Brodeur made 25 saves and was also credited with an assist on the game-tying goal early in the second period by Alexi Ponikarovsky, who was acquired in a trade with Winnipeg earlier in the week.
Flyers goaltender Ilya Bryzgalov faced only 18 shots in the game and allowed four goals.