Nicklas Backstrom scored the only goal of the shootout, and the Capitals rallied from a two-goal deficit to beat the Red Wings 4-3 on Friday night.
It was Detroit's seventh consecutive home loss and its 11th straight overtime loss at Joe Louis Arena.
"Very surprising. It just goes to show you how fickle the game is," said Washington coach Adam Oates, who began his Hall of Fame playing career with Detroit in the mid-1980s. "The same team could win a zillion in a row."
The Capitals rallied from a 3-1 deficit in the third period to tie the game and send it into overtime.
"It's a huge win. That's a good team," said Ovechkin, who trimmed the led to 3-2 early in the third. "Everyone knows what they have out there and how good they are. They got a 3-1 lead, and we kept pushing."
"Same thing, same outcome, but we can't get frustrated, can't get discouraged," Howard said. "Somehow, some way keep a positive mind frame in here and just continue to keep going out there and working because we're doing a lot of good things.
"It's tough to take over a game for a full 60 minutes. There's going to be waves and ups and downs. Mistakes happen; we're just going to have to find a way to overcome them."
Latta tied it 3-all with 8:06 left in regulation when he poked in a loose puck from just outside the slot.
"Obviously nice to get it when it meant so much, and not a 7-0 game," Latta said.
Ovechkin had brought Washington within 3-2 at 3:19 of the third period with his 15th goal. He beat Howard with a one-timed shot from the bottom of the left circle.
DeKeyser's power-play goal with 18 seconds remaining in the second period gave Detroit a 3-1 lead. He put in a one-timed shot from the right circle for his second goal.
Holtby made a spectacular toe save -- with the puck right along the goal line -- on Tomas Tatar's wraparound attempt with 5:50 left in the first period.
Laich opened the scoring 5:50 into the game when he backhanded in his own rebound after skating in off the right wing following a turnover by DeKeyser in the neutral zone.
Franzen then scored twice to put Detroit ahead.
His power-play goal with 4:08 left in the first tied it at 1. He beat Holtby with a screened snap shot from the left circle. Franzen struck again with 2:18 left when he put in a one-timed shot from the bottom of the left circle for his fourth goal of the season.
Red Wings RW Daniel Alfredsson was a late scratch because of a sore groin. ... Capitals D Mike Green didn't play due to a lower-body injury. ... Detroit D Jonathan Ericsson returned after missing 10 games with a separated shoulder. ... Washington D Steve Oleksy is from the Detroit-area suburb of Macomb. ... Red Wings RW Patrick Eaves cleared waivers Friday and was sent to Grand Rapids of the AHL. Detroit also sent C Luke Glendening to Grand Rapids. ... Capitals rookie RW Tom Wilson and backup goalie Michal Neuvirth both played junior hockey with the Ontario Hockey League's Plymouth Whalers, who are based in suburban Detroit. ... Red Wings C Stephen Weiss missed his third game with a sore groin.