Nick Perbix extended the lead to 3-0 at 11:12 when his shot deflected in off the skate of Capitals defenseman Erik Gustafsson.
Sergachev's second goal came on the power play at 16:22 to make it 4-0.
"I think it was the worst 20 minutes I've seen us play this year," Eller said. "We were [terrible], flat out. We acted like we were top of the standings and won 10 in a row. You have to bring a whole different attitude, effort, battle, mentality. ... They just ran right over us."
Sheary made it 4-1 at 18:04 of the second off a pass from Evgeny Kuznetsov.
"After the first period we settled down a little bit," Lindgren said. "Obviously, it wasn't perfect, but our game was better. That first period was tough to watch, and then I thought we got better."
Cole Koepke scored his first NHL goal to make it 5-1 at 13:15 of the third. His backhand in front deflected in off the post and hit the camera in back of the net.
"It feels great, it's something I looked forward to," said Koepke, who was playing in his 13th NHL game. "It's been 12 or 13 games now, so you try not to let it frustrate you, but it finally came and it feels great."