Oshie started by beating Howard, who had 39 saves through overtime. Gustav Nyquist was denied by Braden Holtby on the other end, and Kuznetsov followed with an easy goal off a deke to his right.
Pavel Datsyuk then missed for Detroit, giving the Capitals the win.
"Just two good moves. It’s just too bad," Howard said. "Would have liked to pick up the extra point."
Despite the loss, the Red Wings earned a point in an 11th straight game (8-0-3) in their longest streak since 2010.
"I think when you get to overtime, when you get to shootout you’re leaving it to chance a little bit," Red Wings coach Jeff Blashill said. "That’s the reality of life sometimes. So I think with (Howard) I’d focus on the fact that he did a great job and I don’t think we get the point if he doesn’t play great."
Justin Williams scored in the opening minute for Washington, which extended its point streak to eight games.
This was only the Capitals’ second shootout of the season, and coach Barry Trotz welcomed the opportunity.
"Everybody talks about the shooters, but we’ve got a pretty good goaltender and we feel confident if we get to that point," Trotz said.
Henrik Zetterberg and Tomas Jurco scored for Detroit. Ten of the Red Wings’ last 11 games have been decided by one goal, as have each of their three games with the Capitals this season.
"Howie played well tonight. Kept us in the game," Zetterberg said. "They had a lot of shots, but I don’t know about scoring chances."
The Red Wings forced overtime despite being outshot 39-21 in regulation, allowing four power plays and never working with the extra man.
Down 2-1, Washington pulled even with Detroit’s Brendan Smith in the penalty box. With the puck loose in the crease and two Capitals desperately trying to shove it home, Ovechkin joined the fray and knocked it into the left side of the net.
Though Washington owned a 28-15 advantage in shots on goal after two periods, solid goaltending by Howard made up for the difference.
Detroit used the hustle of Joakim Andersson and deft stickhandling by Jurco to break a 1-1 tie at 3:16 of the second. Andersson outskated Washington’s Dmitry Orlov to secure a loose puck along the back boards, and then sent a pass to Jurco in front of the net. After feigning left, Jurco scored from the right side.
It was Jurco’s first goal of the season and 12th in 106 career games.
Seeking their fifth straight home win, the Capitals took a 1-0 lead when Williams scored with 43 seconds elapsed, the team’s quickest goal of the season.
Washington took six shots before Detroit tested Holtby for the first time, but the Red Wings pulled even at 15:40 when Zetterberg converted a centering pass from Dylan Larkin after Detroit won a faceoff in the Washington end.
Notes:Detroit D Mike Green returned to Washington for the first time since signing with the Red Wings as a free agent in July following a 10-year run with the Capitals. The sellout crowd gave Green a standing ovation following a video tribute during the first period. … Datsyuk played in his 900th career game. … Nicklas Backstrom became the 18th player to play in 600 games with the Capitals. … Holtby joined Olie Kolzig and Don Beaupre as the only goalies to play in 200 games with Washington. … Williams picked up his 600th career point and Marcus Johansson tallied No. 200 with their collaboration on Washington’s first goal.