Haula took a drop pass from Dawson Mercer and beat Carter Hart glove side from the top of the left circle.
Alexander Holtz and Curtis Lazar also scored, and Vitek Vanecek made 28 saves for New Jersey.
Wade Allison and Rhett Gardner scored, and Hart made 19 saves for Philadelphia.
Allison gave the Flyers a 1-0 lead at 2:04 of the first period, finishing a return pass from Bobby Brink in front.
Lazar tied it 1-1 at 8:38, and Holtz gave the Devils a 2-1 lead at 16:42.
Gardner tied it 2-2 at 16:54 of the third period.
