Mike Webber fired a slapper that knocked off Michael Leighton's pad. Ennis swooped in from the right side and scored his second goal of the game.
Game 6 is Sunday in Buffalo.
The Sabres survived after blowing a 3-0 and chasing Flyers starting goalie Brian Boucher.
Thomas Vanek and Marc-Andre Gragnani also scored in the first period for the Sabres, and Ryan Miller made 36 saves. Danny Briere tied it for Philadelphia at 3:36 of the third period. James van Riemsdyk and Andrej Meszaros scored in the second.
ANAHEIM, Calif. (AP) - Jerred Smithson scored 1:57 into overtime, and Nashville moved to the brink of winning a playoff series for the first time, beating Anaheim to take a 3-2 series lead.
Captain Shea Weber tied it on a long slap shot with 35.3 seconds left for the Predators, who had never even won three games in a series before their dramatic comeback stunned the Ducks.
Both teams scored two goals apiece in a thrilling third period, with Anaheim blowing two leads. Bobby Ryan scored a spectacular goal early in the third in his return from a two-game suspension, but Joel Ward tied it with 8:40 left. Jason Blake put Anaheim ahead on his second goal with 5:44 left.
Game 6 is Sunday in Nashville.