Yakemchuk one-timed a shot from the point that went clean past Joseph Woll on the power play to give the Senators the 2-1 lead.
Linus Ullmark made 28 saves, and Nick Cousins also scored for the Senators (3-1-0).
Matvei Michkov scored for the Flyers (0-3-2), who opened the season with five straight losses. Woll made 24 saves.
Cousins gave the Senators a 1-0 lead at 10:14 of the first period, tipping a Tyler Kleven shot from the point past Woll.
Michkov tied the game 1-1 at 7:46 of the second period on the power play. After a shot from Trevor Zegras trickled through Ullmark's pads, Michkov tapped in the loose puck on the backhand.
Ottawa forward William Eklund was helped off the ice with a lower-body injury in the first period after being hit awkwardly into the boards by Flyers defenseman Simon Benoit. Eklund was unable to put weight on his left leg as he went down the tunnel and did not return.
