Dan Vladar made 25 saves for Philadelphia (1-6-3), which avoided becoming the 11th team in NHL history to lose its first 10 games of a season.
Drake Batherson scored for Ottawa (6-3-0). Linus Ullmark made 25 saves.
Batherson put the Senators ahead 1-0 at 5:55 of the second period, finishing a 2-on-1 rush with Claude Giroux.
Martone tied the game 1-1 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.
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 to Michkov, who tapped the rebound behind Ullmark.
Trevor Zegras made it 3-1 with an empty-net goal at 19:46.
Philadelphia forward Owen Tippett missed the game because of an upper-body injury.
