The Stanley Cup playoffs are more often a test of will and patience than of sheer skill. Games often hinge on the slightest mistake, and the anticipation for that game-altering play can make even the most grizzled spectator sick to his stomach.

Game 2 of the first-round NHL playoff series between the Washington Capitals and New York Rangers at Verizon Center on Saturday afternoon was one of those games. Every gaffe contained devastating potential and every shot represented a possible game-winner as the teams played more than 60 scoreless minutes before the visitors’ pivotal mistake.

Mike Green scored on a power play eight minutes into overtime to give Washington a 1-0 win and a 2-0 lead in this best-of-seven series.

The goal was the latest work of “game-over Green,” the moniker the defenseman earned once again with the 18th game-winning goal of his career — eight of them in overtime. But the opportunity for Green to coolly blast a shot from the top of the circles past Henrik Lundqvist first required a costly penalty by Rangers defenseman Ryan McDonagh.

“I think the whole game was patience — whoever was going to make the mistake first,” Green said. “Just a lucky one tonight. What an effort before we got that power play by the guys that were on the ice, pressuring their D. They had no choice but to try to go off the glass and they made a bad play.”

Track every shot in the Capitals’ playoff games, see which ones they made count, and view by player, goals and ice strength.

Shortly after killing a penalty of their own in overtime, the Capitals hemmed New York deep in its own zone, forcing the visitors to keep an increasingly tired group on the ice. McDonagh had been on for a shift lasting 3 minutes 4 seconds when he attempted to clear the puck out of the zone but instead sent it over the glass to earn a minor penalty for delay of game.

Washington dominated overtime even before McDonagh made his way to the penalty box. The Rangers failed to muster a shot on goal in the extra session despite a power play that started 1:15 in when Capitals defensman Steve Oleksy committed the same delay-of-game infraction.

The Capitals penalty killers blocked shots aggressively — perhaps no one more so than Eric Fehr, who dove in front of an attempt by Derick Brassard immediately after a shorthanded chance — and barely allowed the Rangers to set up on the man advantage. New York finished the game 0 for 3 on the power play.

“I was telling a few guys this might have been our best PK game all year,” said Capitals goaltender Braden Holtby, who recorded 24 saves for his first career playoff shutout. “You could tell we were confident going into overtime. We were prepared and the big kill got us fired up out there. [We] used it to our advantage and the guys kept pounding away down in the offensive zone and finally got one.”

Boosted by the dominant penalty kill, the Capitals focused renewed energy on trying to beat Lundqvist, who was superb in a 37-save outing. New York’s celebrated netminder stopped far more challenging shots than Holtby over the course of the game, including a save on a tip by Mathieu Perreault, backdoor shots by both Marcus Johansson and Nicklas Backstrom at the end of tic-tac-toe plays, and a late opportunity in regulation by Jason Chimera in front.

“Lundqvist has played really unbelievable all game. He was making saves that most guys wouldn’t. You can’t let up and think something’s going in until it does,” Troy Brouwer said. “We know that if we keep pushing in waves, and we continue to get more chances and more chances, finally one’s gonna go in at some point. It was good that the guys stuck with it, and we didn’t get frustrated with it.”

McDonagh’s never-ending shift started with 4:05 gone in overtime and the Capitals’ top line pressing for a goal. The Capitals’ second line of Martin Erat, Mike Ribeiro and Brouwer extended the time in the offensive zone, forcing New York to ice the puck. A fresh third unit of Perreault, Chimera and Fehr took over, churning through another shift in the Rangers’ end until Lundqvist froze the puck.

When Alex Ovechkin, Backstrom and Johansson emerged from the bench for the faceoff, McDonagh, whom Rangers Coach John Tortorella matches against the opponent’s top line, remained on the ice. Washington’s stars executed another dominant shift with three shots on goal until McDonagh shot the puck over the glass on a clearing attempt.

The Capitals’ power-play unit finished with a league-best 26.8 percent success rate in the regular season, and scored in Game 1 .

“We kind of get a little bit giddy, like a kid, when we get the power play,” Green said.

Ribeiro made a savvy decision to fake a shot at the top of the right circle, leaving space for Green at the top of the zone as two Rangers penalty killers went down in an attempt to block.

For as many talented players as the Capitals have on their roster, there may be no better player to have with that opportunity in overtime than Green. The 27-year-old defenseman blasted a shot that deflected off the stick of Rangers forward Derek Stepan and found the back of the net.

“He’s a big-time player. He handles the pressure well,” Karl Alzner said. “He’s calm all the time with the puck in regulation. So when it gets into overtime and guys start to get the shakes a little bit, he’s still calm Mike Green. [He] just is able to find those holes and it really is amazing.”