Ovechkin tied it 2-2 with 6:10 remaining when he redirected a pass from T.J. Oshie, made it 3-2 with 5:00 left when he knocked in his rebound after Jonathan Quick saved his shot from the point, and scored into an empty net to make it 4-2 with 1:46 left for his 40th goal of the season and No. 698 in his NHL career.
"That's impressive and just tonight sums it all up: In less than five minutes, he took over the game," Capitals coach Todd Reirden said. "We win the game because of that. That's what superstars do. … This is a real, real special player."
[WATCH: All Kings vs. Capitals highlights]
John Carlson scored for Washington (36-13-5), which has won six of its past eight. Braden Holtby made 29 saves.
"[Holtby] came up big," Carlson said. "As we do, we gave up a lot of chances there for a little stretch and kind of got our head on straight again and started to simplify it and not giving them anything good to thrive off."
Jeff Carter scored twice for Los Angeles (19-30-5), which is 1-6-1 in its past eight games. Quick made 20 saves.
"It's happened all year to us," Kings defenseman Drew Doughty said of losing the lead in the third period. "We've got to win those games. That's the bottom line. We win some of those this year, even half of them, I bet you we're only five points out of a playoff spot."
Video: LAK@WSH: Carlson wrists puck home on rush
Ovechkin, who has 14 goals in his past seven games, didn't have a shot on goal until his first goal, which came after Oshie was moved to a wing with Ovechkin and center Nicklas Backstrom.
"Obviously, it was a tough couple periods for our line, but when [Oshie] jumped in you can see we started to create some moments out there, and the first one was a pretty pass and I got lucky it bounced off my stick and goes in," Ovechkin said.
Carter, skating out from behind the Capitals net, deflected a pass from Doughty to give the Kings a 2-1 lead at 11:33 of the third. Doughty, who missed the previous three games with an injury, passed Rob Blake for most points by a defenseman in Kings history (495).
"Growing up you never even think you're going to make the NHL, so I've never thought of this moment in my whole life until recently, just kind of being aware of it," Doughty said. "But [Rob] was one of my favorite defensemen growing up, he's a Hall of Famer, he's our [general manager] right now and to pass him ... it's just such an honor."
Carter gave the Kings a 1-0 lead at 15:03 with a wrist shot from the left circle.
Video: LAK@WSH: Carter snaps puck past Holtby
Carlson, the trailer on a 3-on-2, took a cross-ice pass from Backstrom and scored with a wrist shot from the right circle at 7:25 of the second period to tie it 1-1.
Ovechkin leads the NHL with 40 goals. He and Wayne Gretzky are the only players to have at least 11 40-goal seasons in the NHL (Gretzky had 12, including his final three with the Kings).
"There's a reason why he's got [almost] 700, and give him a couple more years and he'll be at 800," Los Angeles coach Todd McLellan said of Ovechkin. "It's that type of night where maybe you don't see him a lot early and then bang, bang, bang and it's in the net and they've won."
Video: Clutch Performance: Ovechkin nets a hat trick
They said it
"Give [the Capitals] credit. They believe in what they're doing and they're patient. They wait for mistakes and then they capitalize. Good teams do that. We're not good enough right now to make mistakes or give up a freebie and overcome it. The difference between the two teams is exactly that." -- Kings coach Todd McLellan
"To shut down the best scorer in our generation by a mile for 55 minutes and then let him get three in the last five or whatever the minutes were, it's really frustrating." -- Kings defenseman Drew Doughty
"Just sometimes you're not getting everything you're looking for. You just want to change a little of the chemistry for a bit. And obviously on the night, it worked out. We force an icing, so I'm able to put Backstrom, Ovi and [Oshie] on the ice. And we get a matchup that they don't want, so that was fortunate. And then we're able to convert on that one to get us back in it." -- Capitals coach Todd Reirden
Video: Enterprise Hat Trick: Ovechkin scores three vs. Kings
Need to know
Ovechkin tied Brett Hull and Teemu Selanne for fourth in NHL game-winning goals (110), behind Jaromir Jagr (135), Gordie Howe (121) and Phil Esposito (118). ... It was Carter's first multigoal game since he scored twice against the Vancouver Canucks on Oct. 30. ... Doughty has 116 goals and 379 assists in 903 games with the Kings. ... The last NHL player to score three goals in the final seven minutes of a third period was Peter Bondra of the Capitals on March 26, 1996, in a 7-1 win against the New York Islanders. ... Ovechkin would become the eighth player in NHL history to score 700 goals (Gretzky (894), Howe (801), Jaromir Jagr (766), Brett Hull (741), Marcel Dionne (731), Esposito (717), Mike Gartner (708).
Kings: At the New York Islanders on Thursday (Barclays Center, 7 p.m. ET; MSG+, FS-W, NHL.TV)
Capitals: Host the Philadelphia Flyers on Saturday (7 p.m. ET; ESPN+, NBCSWA, NBCSP, NHL.TV)
Video: Ovechkin moves closer to 700 goals in Capitals win