Drake Batherson scored for Ottawa (6-3-0). Linus Ullmark made 25 saves.
"Hard to win in this league when you don't have all 23 guys going and tonight we didn't have everyone going," Senators forward Warren Foegele said. "They were more desperate tonight and it showed."
Batherson put the Senators ahead 1-0 at 5:55 of the second period, finishing a 2-on-1 rush with Claude Giroux.
But rather than wilt after allowing the game's first goal for the eighth time in 10 games, the Flyers pushed and got a tying goal from Martone at 9:03. He poked a puck away from Senators defenseman Thomas Chabot in the Ottawa zone, and Michkov was first on the loose puck. His shot-pass from the left side went off Martone's stick and past Ullmark in the crease.
"I think we had a lot of momentum," Martone said. "We were on them and our line gets scored on there, and I think 'Catesy' (Noah Cates) says it on the bench, we got one back here, and I think it was next shift that we scored. I think we got a lot of good leaders in this room, a lot of people on this team that can kind of pull people into the fight, and I thought that everyone did a great job of that today, and that's a big win for us."
Offense has been tough to come by for the Flyers, who had scored 11 goals in their first nine games, and Saturday was the first time they scored more than two.
Martone and Michkov also were the first Flyers forwards to have a multipoint game this season.
"I think I've said it all along, our team goes with the young guys and the steps that they take and are going to continue to take," Philadelphia defenseman Travis Sanheim said. "It's obviously positive just to see that tonight, and hopefully it continues."
Michkov put the Flyers ahead 2-1 with a power-play goal at 18:33. Martone's shot from the left side went off Ullmark's left pad and Flyers forward Michael Bunting in front of the net to Michkov, who tapped the rebound behind Ullmark. The assist was Bunting's first point with the Flyers.
"That was our third game together, so I think we're kind of starting to read off each other, see our tendencies, see what we like," Martone said. "I liked the show tonight. I think we're two very skilled players, and I think as time goes on and we kind of develop more chemistry, I think we can bring a lot to this team."