Drysdale tied it 1-1 at 3:05 of the second period when his backhand from the slot bounced off Forsberg and in.
The defenseman has goals in consecutive games for the first time in his five NHL seasons after he had a goal in a 3-1 loss to the New Jersey Devils on Sunday.
"I feel pretty confident in my game," he said. "But in saying that, as a team we've got to win and I can still be a lot better. Made a bunch of mistakes defensively, caused a couple chances against."
Kleven put Ottawa ahead 2-1 at 4:14 when he corralled a bouncing puck at the left point and scored through a Drake Batherson screen. It was his first goal in 20 games.
"Always good to pitch in when I can," he said. "The puck was just bobbling there, and I just threw it on net, a little knuckle curve and it went in."
Abols tied it 2-2 at 8:45 from the left face-off circle.
Amadio made it 3-2 at 15:01 with a shot along the ice from the right side.
"We're trying to get traction, we're trying to get momentum and they score right after," Flyers coach John Tortorella said. "Especially the third one, that hurts. ... The third goal took the wind right out of our sails after we get it tied up."
Cozens scored for the second time in three games with the Senators to make it 4-2 at 10:59 of the third period. The forward was acquired in a trade with the Buffalo Sabres on Friday.
"He's a nice player," Green said. "He's very coachable. He's hungry to win. He's made a good first impression on us for sure. ... He's kind of just fit right in. He's a big body, skates probably better than I imagined, and he's been physical. I think he had 17 hits in his first two games, and gets a couple big goals as well."
Pinto scored an empty-net goal at 19:25 for the 5-2 final.
NOTES: Tkachuk's goal was his 189th, passing Marian Hossa for fourth all-time for the Senators. ... Cozens' goal was his 200th point in the NHL. He has three points (two goals, one assist) during a three-game point streak since joining the Senators; the only players in the past 10 years with as long a point streak to begin their time in Ottawa are Chris Tierney (seven games, 2018-19) and Batherson (three games, 2018-19). ... Tim Stutzle had his 202nd assist on Tkachuk's goal, tying him with Hossa for 10th all-time for Ottawa. ... Flyers defenseman Cam York had an assist on Abols' goal for his first point in eight games. It also gave him six points (three goals, three assists) during a five-game point streak against the Senators. ... The Flyers lost their fifth straight at home, tying for the second-longest in franchise history; it's happened four times, most recently in 2021-22. The team record is eight straight in 2006-07.