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.

So far, it doesn't look good for the fourth-year coach.

Ottawa, which had lost four straight, scored three late goals and jolted the Flyers, 4-3.

Matt Duchene batted in his own rebound with 2 minutes, 59 seconds left to snap a 3-3 tie. It was the Senators' third goal in a 5:29 span, erasing a 3-1 deficit.

"Unacceptable," said defenseman Radko Gudas, who scored his first goal in 47 games. "After two periods, I thought we had them. I thought we played pretty good hockey and had a grip on the game. We're making soft plays around the blue line and that cost us the game."

Brady Tkachuk scored a pair of late goals 1 minute, 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. With 6:34 remaining, after a Shayne Gostisbehere miscue, he deflected Thomas Chabot's point drive past goalie Anthony Stolarz, who was aiming for his first NHL win in almost two years.

"We just gave it away," right winger Jake Voracek said. "As soon as they got the second goal, we kind of got scared. You can't do that or every single team is going to jump on it and gain the momentum, and that's what they did. … I still don't know what happened. I can't believe we lost that game."

Voracek said: "It's just the way it's going now. Everything we touch, just doesn't work. … It's like we got scared, started slamming pucks everywhere along the ice instead of just holding it. As soon as you start whacking pucks and standing still, that's trouble, and I think that's what we did in the third period."

The Flyers got goals from Travis Konecny, Voracek, and Gudas, but they lost for the sixth time in the last seven games. Loud boos echoed around the arena as they left the ice.

They are just 5-7-1 at home.

Voracek said the Flyers are making "mistakes by a team that doesn't have confidence, which we don't have right now. And there's nobody to blame but ourselves. We put ourselves in that position. [Up] 3-1 against a team that played yesterday, no matter what kind of position you're in mentally, you have to find a way to win ."

Defenseman Ivan Provorov, who was reunited with Shayne Gostisbehere for most of the game, and Scott Laughton each had a pair of assists for the Flyers. No matter. They lost despite outshooting the Sens, 37-24.

Earlier in the day, Paul Holmgren, the Flyers' club president, said Hakstol's future will be decided by the new general manager.

"Given the scenario we're in, that's a pretty reasonable process," Hakstol said before the game. "They'll make a hire on a new GM, and whoever that is will come in and evaluate me as a head coach and whether or not he likes what he sees and if I'm the right guy to work with him."

Asked about his performance this season," said Hakstol, whose team  is 10-12-2 and at the bottom of the Metropolitan Division standings, said, "Nobody is happy with where we're at. [Monday] was a tough day for everybody inside our organization and inside of our dressing room, so we show up and work and battle every day….We have to find ways to make our team a little bit better."

The Flyers looked in control as they took a 3-1 lead into the last period against Mike McKenna, a backup goalie who had a 5.41 goals-against average in his first four appearances, contributing to the Senators' league-worst 4.33 GAA.

Cue the late-game collapse.

"After two good periods, we didn't push pucks deep and do the things that got us to that point," Hakstol said.

Breakaways

Michael Raffl, used at  right wing on the fourth line, came off the injured list and played his first game since Oct. 22. … Hakstol said injured goalie Brian Elliott's status was "week to week."… Laughton entered the night leading the NHL in faceoff percentage (63.5).