Travis Konecny, Jakub Voracek and Gudas scored for Philadelphia (10-12-2) in its first game since general manager Ron Hextall was fired Monday.
Stolarz made 20 saves. He's the NHL-high fifth goalie to start a game for the Flyers this season, after Brian Elliott (13 starts), Calvin Pickard (eight), Michal Neuvirth (one) and Alex Lyon (one).
Tkachuk scored twice in 1:54 in the third to tie the game 3-3. He tapped in a loose puck on the post to Stolarz's left at 11:32 to get Ottawa to within 3-2, and then tipped a Chabot shot at 13:26.
"He brings something a little different," Duchene said of Tkachuk. "We don't have a power forward quite like him on this team. When we drafted him, I was excited to have a guy like that.[With the Colorado Avalanche], I played with Gabriel Landeskog and I told him before the game they're very similar players in the stuff they do. ... Brady crashes and bangs, he's got good hands and good feet, and he can see the ice at the same time. Obviously, you can see why he was such a high pick for us (No. 4 in 2018 NHL Draft)."
Tkachuk has eight points (five goals, three assists) in the past six games and 10 points (six goals, four assists) in 10 games back after missing nine with a leg injury.
"Before I got hurt, I thought I was playing well," he said. "It's unfortunate but it's part of the game, getting hurt. My mindset was come back and be better than I was. Tough start coming back, but really felt like I've improved my game every day."
The Flyers took a 3-1 lead on Gudas' goal at 6:00 of the second period and were outshooting the Senators 27-15 entering the third. The loss was their sixth in seven games (1-5-1).