Pittsburgh's Alex Kovalev scored the first shootout goal. He was matched by Philadelphia's Danny Briere. Kunitz got the final shootout attempt through the legs of Sergei Bobrovsky for the winner.
Philadelphia's Mike Richards and Pittsburgh's Tyler Kennedy scored goals in regulation.
The Flyers played in their fourth straight shootout and reached overtime for the fifth time in six games. They have won only one of those games that needed extra time and are losing their grip on the Eastern Conference lead.