Ilya Lyubushkin gave the Sabres a 1-0 lead at 4:43 of the first period on a wrist shot from the right point through a screen by Kyle Okposo.
Peterka extended it to 2-0 at 8:50 when Jack Quinn broke out 2-on-1 off a defensive-zone face-off, toe-dragged past van Riemsdyk and slid a pass to him for the tip-in.
Oshie cut it to 2-1 at 10:03, knocking in the rebound after Dylan Strome hit the post during a power play.
Tyson Jost responded at 18:06 to make it 3-1. After Casey Mittelstadt forced Conor Sheary to turn over the puck, Jost collected it and scored stick side from the slot.
"We were just playing to our identity, playing the way we know how and being patient, but also playing with quickness and five in the picture," Jost said. "We like the way we started. Obviously, it stings right now, so it's a tough one. There's definitely positives. It's just tough to kind of find [them] right now."
Kuznetsov and Oshie scored in the shootout for Washington.
"It was really good," Capitals coach Peter Laviolette said. "It was a team effort. We need everybody on that rope and pulling things in our direction. There's no question our big guys had some bug games."
NOTES:Washington defenseman Nick Jensen left the game in the third period (undisclosed injury). Laviolette did not have an update after the game. … Luukkonen is 0-2-2 in his past four starts. His last win was Feb. 26 against the Capitals. … Strome has 10 points (three goals, seven assists) during a six-game point streak. … Ovechkin had one goal, one assist, five shots on goal and one hit in 19:32 of ice time after missing one game with a lower-body injury. He has 402 goals at home, surpassing Mike Gartner for fourth place on the NHL's all-time list. … Krebs has 22 points (eight goals, 14 assists) in 59 games this season, tying his career high set last season in 48 games.