Yeo said he had a feeling Atkinson (5-foot-8, 176 pounds) was due for a big game after seeing him take a lighthearted run at defenseman Rasmus Ristolainen (6-4, 221) during practice Friday.
"He's such a competitor, he's such a warrior," Yeo said. "It's a lot easier to come to the rink if you're having fun, you're enjoying yourself, to go out there and perform. Especially for a guy like that who wears his emotions on his sleeve.
"I felt pretty good that he was going to come out and play well today and I was happy to see him get rewarded in the first period."
Oshie scored on the power play to make it 2-1 at 6:53 of the second period. It was his second game after missing 14 with an upper-body injury, and his first goal since Jan. 10.
That energized the Capitals, who outshot the Flyers 16-5 the rest of the game, including three shots on goal and nine shot attempts in the final 2:02 with Samsonov out for an extra attacker.
"That first period is something we want back," Washington forward Carl Hagelin said. "Can't let that happen, the way they dominated us in the first. Dig yourself a hole like that, it's hard to come back. It doesn't matter how well you play the rest of the game."