Minnesota earned its second straight win despite being outshot 30-11, becoming the first team since the NHL officially began tracking shots on goal in 1973-74 to score five goals on fewer than 12 shots, according to the Elias Sports Bureau.
Suter completed his first career hat trick with the biggest goal of the game, putting the Wild ahead 5-3 seconds after Minnesota had killed off an opportunity for Washington's power-play unit, which ranks No. 2 in the NHL.
"I came out of the box and saw some of their guys were changing there and Stony made a great play getting the puck over," Suter said. "I was hoping he was going to pass. I was just hoping I didn't miss the net."
Minnesota shut out Ovechkin, the NHL's leading goal scorer with 31. Ovechkin hit the post in the final minute as the Capitals tried to rally from a two-goal deficit.
"We're going through a lousy stretch right now where we're playing some good hockey and getting some lousy results," Capitals coach Adam Oates said. "Eleven shots (allowed) on the road should be good enough. But it's not, so we need to find a way to play just a little bit better."
Washington controlled the action early on, outshooting Minnesota 11-1 in the first and taking a 2-0 lead with two goals in a 13-second span midway through the period.
Johansson pushed a rebound past Minnesota goalie Niklas Backstrom for a power-play goal. Then off the ensuing faceoff, Jason Chimera picked up a loose puck at the Minnesota blue line and passed to Green, who made a move around Minnesota's Matt Cooke and beat Backstrom with a wrist shot from the top of the right faceoff circle.
"The first period, I really don't think we could've scripted that any better," Capitals centre Brooks Laich said. "Two-nothing lead, they have one shot, they're not in our zone, they're getting booed off the ice after 20 minutes by their own fans on a Saturday night. We're in total control of that game."
But the Wild rallied in the second, thanks to a couple of ill-timed penalties by the Capitals. Suter scored twice on the same power play after the Capitals took two minors in four seconds. He tied the game on a wrist shot from between the circles with the Wild on a 5-on-3 advantage. He then gave Minnesota the lead 42 seconds later when his shot from the same spot on the ice slipped past a screened Holtby, erasing the sour taste left by the game's first 20 minutes.
"Yeah, first period was terrible," Suter said. "(We) didn't have a lot of energy. We came in here, got yelled at, and went out and played the way we needed to play. (Dany Heatley) did a good job on those two power-play goals. He was in front of the goalie and he couldn't even see the puck. The little things are making the difference."
Green caught a break with an odd bounce for his second goal of the night, tying it at 3. Off a faceoff, he flipped the puck off the end boards, but it caromed off Backstrom's left skate and into the net.
"Putting it in the stands - we talk about details all the time and we get two of them tonight and they score on both of them," Oates said. "It's just frustrating in general, for all of us."
Minnesota snapped a franchise-record six-game losing streak with a 4-1 win over Buffalo on Thursday. Now it heads West for a road trip with a little momentum after the victory over the Caps.
"When you have that consistency in your game, that's when you get consistent results, and so that's our challenge now," Wild coach Mike Yeo said. "We have to come into our next game and we have to be determined to be better than we were tonight."
NOTES: Ovechkin's assist in the first-period was the 376th of his career, passing Dale Hunter for third place on the Capitals' franchise list. ... The Wild put D Jared Spurgeon on the IR with a lower-body injury and recalled RW Brett Bulmer from Iowa of the AHL to replace him on the roster. ... After going 40 games without a goal this year, Suter now has five in his last four games.