Evgeny Kuznetsov had two assists for the Capitals (40-19-6), who won on the road for the first time in five games and lead the Philadelphia Flyers by three points for first place in the Metropolitan Division.
"I think both teams was really hungry for those points, and I think they need it as much as we need those points," Kuznetsov said. "I think we played a great job. They dump a lot of pucks, and I think we got close support, all five guys coming back. That's what gave us success today."
WATCH: [All Capitals vs. Wild highlights]
Braden Holtby made 37 saves for Washington, including 16 on 17 shots in the third period.
"It was a hard one. [Minnesota] worked hard. Really hard," Holtby said. "[Coach Dean Evason's] got them buzzing over there, so good challenge. It was a good, hard-fought game. We'll take two points, but it wasn't easy."
Kevin Fiala had a goal and an assist for the Wild (32-26-7), who lost for the first time in four games and trail the Nashville Predators, Winnipeg Jets and Arizona Coyotes by one point for the second wild card into the Stanley Cup Playoffs from the Western Conference. Alex Stalock, in his fourth straight start, made 26 saves.
"It felt like a playoff game," Fiala said. "We were fighting from the start to the end. It didn't go our way."
Ryan Donato got to the puck behind the net after he missed a shot on a breakaway and banked it in off Holtby's left skate to give Minnesota a 1-0 lead at 3:01 of the first period.
Ovechkin tied the game 1-1 with a one-timer from above the left face-off circle on a 5-on-3 power play at 7:21.