In their first game after general manager Ron Hextall was stunningly fired on Monday, the Flyers started the Save Dave Hakstol's Coaching Job portion of their schedule Tuesday at the Wells Fargo Center.
The way the Flyers play in the coming days, and the days after a new GM is hired, will likely decide Hakstol's fate.
Ottawa, which had lost four straight, scored three late goals and jolted the Flyers, 4-3.
Brady Tkachuk scored a pair of late goals 1 minutes and 54 seconds apart to tie the score at 3-3. He knocked in a rebound with 8:28 left in regulation to get the Senators to within 3-2.