Noesen's power-play goal made it 1-0 at 4:27 of the first period when he redirected Burns' shot from the left point for his first goal with the Hurricanes.
"I kind of take pride in that," Noesen said. "It's something I work on all the time. I always want tips. It's something I love doing."
The goal came on the first of six Carolina power plays.
"They scored on their first opportunity, which is sometimes tough for the guys, but we dug in," Kuemper said. "[We] probably had a few more kills than we wanted to, but we were able to kill them off. That was huge tonight."
Strome tied it 1-1 at 1:23 of the second period. Andersen stopped Nick Jensen's shot, but Strome got position on Sebastian Aho at the top of the crease to score on the rebound.
"I was kind of alone in front of the net there with Aho, then tipped it a bit and it was just sitting there," Strome said. "It got us back into the game. Big goal at the time."
The Capitals scored on the power play to take a 2-1 lead at 8:57 when Erik Gustafsson set up Ovechkin for a short-side one-timer from the left face-off circle.
Ovechkin's goal was the 785th career of his NHL career, bringing him to within one of Gordie Howe's (Detroit Red Wings) single-team goal record.
Svechnikov, who also scored the winning shootout goal, tied it 2-2 at 15:42. Paul Stastny redirected a shot from Necas, and Svechnikov jumped on the rebound.
He is tied for second in the NHL with eight goals; Edmonton Oilers center Connor McDavid has nine.
"I thought it was a really hard-fought game," Carolina coach Rod Brind'Amour said. "I'm really happy with it. I like that we stuck with what we were trying to do and didn't really get away from it."