Tyler Ennis had two goals and an assist for the Senators (15-18-4), who have lost three of four (1-1-2).
"I thought we played real hard," Ottawa coach D.J. Smith said. "For the guys we had on the back end, some of the young guys that haven't had a lot of experience in the League, against some elite players, I thought some guys played really hard. I thought, being down 2-0, we just kept playing. And then being down in the third, we found a way."
Marcus Hogberg made 34 saves, including seven in overtime.
"He played great," Ennis said of Hogberg. "All year, whoever's been in the pipes has been great for us, and he's no different. Our goalies have been awesome and are giving us a chance to win every time."
Kevin Hayes took a stretch pass from Voracek, beat defenseman Erik Brannstrom wide, and scored on the power play to give the Flyers a 1-0 lead at 3:16 of the first.