Michkov put the Flyers ahead 1-0 at 17:31 of the first period when he scored on a breakaway.
Ovechkin's goal tied it 1-1. It gave him 1,590 points, tied with Phil Esposito for 11th in NHL history.
"It's really cool getting to be a part of his chase," Chychrun said. "It's been really special for us as a group to kind of see, how big of an accomplishment it could be for him to do what he's doing. We're pulling for him, and he continues to score, continues to produce for us, and it's been a lot of fun."
McMichael put the Capitals ahead 2-1 at 4:17 of the second period when he redirected an Aliaksei Protas pass past Fedotov.
Foerster tipped a shot by Emil Andrae for a power-play goal that tied the game 2-2 at 7:23. The Flyers had been 0-for-10 with the man-advantage in five games.
"It felt good," Foerster said. "'Email' [Andrae] and 'TK' [Travis Konecny, who will represent Canada at the 4 Nations Face-Off] made a good play. That's what we pre-scouted, take one-timers and I was just lucky enough to tip it."
Michkov put the Flyers ahead 3-2 at 11:19 when he tapped in a seam pass by Rodrigo Abols.
The rookie had a chance for a lacrosse-style goal at 4:15 of the third period but Lindgren was able to make the save.
"There was a pre-scout this morning on him doing a similar thing," Lindgren said. "I saw him get it on his stick, and I said, 'Oh boy, I better climb this post here.' Pretty impressive. I thought he was the best player on the ice tonight. He was all over the place, making plays. Obviously a heck of a talent. He's going to be a fun one to watch in this league for a long time."
NOTES: Fedotov is the 180th goalie Ovechkin has scored against. ... Ovechkin has 34 goal streaks of at least four games, tied with Mario Lemieux for the most in NHL history. ... Ovechkin's goal was his 35th against a team coached by John Tortorella, the most he's scored against any opposing NHL coach. ... Michkov had his third two-goal game of the season. ... Capitals forward Taylor Raddysh had two assists. ... Carlson's assist on Chychrun's goal gave him points in five straight games (five assists), matching his season-long streak. ... Capitals forward Dylan Strome had an assist on Ovechkin's goal to give him six points (three goals, three assists) during a five-game point streak.