Thompson made it 3-1 at 5:50 of the second period, receiving a pass from Tuch and scoring on a wrist shot to the far side from the right hash marks.
Ovechkin pulled the Capitals within 3-2 a 16:46. Evgeny Kuznetsov guided a face-off back to Ovechkin, who scored on a wrist shot from the top of the right circle for his 27th goal of the season.
Ovechkin has five goals in his past two games and 28 for the season.
"I think everything was when we start to play hard, we start put puck deep, forechecking well, it kind of opens up in the offense zone," Ovechkin said. "We have very good chances right away in the second period then execute and then score."
Nic Dowd tied it 3-3 when he knocked in the rebound of Milano's shot 55 seconds into the third.
The Sabres wore custom T-shirts in honor of Hamlin before the game. The shirts read "Love for 3," Hamlin's jersey number, in the Bills' red and blue colors. Adams wore a "3" on his lapel.
"It's hard to say much about the game, to be honest," Adams said. "What I can tell you, though, is we talked as a group this morning. We have such good people in our locker room, players, coaches, staff, and it wasn't feeling right this morning. It didn't feel like a normal game day, so we talked about it as a group. I told them, to be honest, how proud I am of them and what they've done in this community through a lot of tough times."
NOTES:Thompson reached 30 goals in 36 games. Only two Sabres reached 30 in a season in fewer games: Alexander Mogilny (30 games in 1992-93), and Pat LaFontaine (31 games in 1991-92). … Thompson has 32 points (13 goals, 19 assists) in his past 21 games, and Tuch has 30 points (11 goals, 19 assists) in his past 21 games. … Oshie played 15:39 and had two shots on goal in his return after missing six games because of an upper-body injury. … Dowd won 18 of 23 face-offs. … Capitals defenseman Erik Gustafsson had his seven-game point streak (six goals, seven assists) end.