Christian Dvorak scored for the Coyotes (8-24-5), who ended a seven-game losing streak (0-6-1) with their sixth win in their past seven home games against the Capitals (6-0-1).
T.J. Oshie and Evgeny Kuznetsov scored for Washington (22-12-2), which lost for the first time in five games. Grubauer made 24 saves.
"We just weren't where we need to be," Capitals coach Barry Trotz said. "I take nothing away from the Coyotes. They played a real strong game today. They stayed with it, they were able to get a late goal and capitalize in overtime, but we had it. We've just got to close it out."
Oshie gave Washington a 1-0 lead at 5:40 of the second period after Kuznetsov intercepted Wedgewood's clearing attempt along the boards on the right side of the Arizona zone. Kuznetsov passed to Jakub Vrana in the slot. Wedgewood stopped Vrana's shot, but Vrana slipped the rebound back to Oshie, who was trailing on the play and beat Wedgewood to the glove side.
Dvorak tied the game 1-1 at 1:28 of the third period on a power play when his wrist shot from the left circle beat Grubauer inside the far post. He has four points (three goals, one assist) in four games against the Capitals.
Washington took the lead back at 4:32 when Kuznetsov slid the rebound of Christian Djoos' shot past Wedgewood on his backhand to make it 2-1. Kuznetsov has seven points (two goals, five assists) in his past five games.
The Coyotes outshot the Capitals 27-17.
"That's a world-class team. They've got Hall of Famers over there, so for me, I liked our defensive effort. We played a really responsible game," Arizona coach Rick Tocchet said. "I thought the whole team contributed tonight."
