Alex Ovechkin was exasperated. The Washington Capitals’ captain had already fired six shots at New York Rangers goaltender Alexandar Georgiev, who had kept each one from whizzing past him and into the net. Ovechkin got a seventh shot at him in the shootout, but as he skated to the net and cut to his right to create an opening, ­Georgiev tossed his stick to knock the puck away from Ovechkin, who was poised to score into the ­empty net.

Ovechkin threw his hands up, confident that Georgiev’s interference meant he would be awarded a goal. The officials huddled and initially announced just the opposite, and to that Ovechkin sarcastically clapped in front of his team’s bench. After a second consultation involving video review, ­Georgiev’s action did result in a goal for the Capitals. And with that bizarre ending in the fourth round of the shootout, Washington had a 3-2 victory to extend its winning streak to four.

“I knew 100 percent it was a goal because it was an empty net,” Ovechkin said.

“Initially, from [the referee’s] vision point, he couldn’t tell for sure that the stick was thrown,” Capitals Coach Todd Reirden said. “He was on the opposite side of the play. The other referee would have seen that more clearly, and it was obvious that it occurred. But then in that situation, it goes to [the NHL situation room in] Toronto on a play like that.”

With a difficult schedule to end the season, including three games against the league-best Tampa Bay Lightning as well as matchups with playoff bubble teams such as the Pittsburgh Penguins and Carolina Hurricanes, Sunday’s matinee represented an opportunity to collect points against a club that is well out of the postseason race. Washington did just that, moving two points ahead of the New York Islanders atop the Metropolitan Division. New York fell, 4-1, to visiting Philadelphia later Sunday; the Islanders have played one fewer game.

“It’s obviously big for us to start playing the right way,” said Capitals goaltender Braden Holtby, who finished with 22 saves. “Obviously, we do have to be realistic with the teams that we’ve played in that stretch and the teams that we have coming up here that it’s going to be a lot different. But we have confidence from this little stretch, and we know we’re going to have to be better playing against some really high-powered offenses, and it’ll be a fun test.”

For the fifth straight game, the Capitals allowed the game’s first goal within the first four minutes. Defenseman Dmitry Orlov turned the puck over in front of Washington’s net, and New York’s Ryan Strome scored from point-blank range 45 seconds in. But the Capitals finished the opening period ahead, thanks to two goals created by their two newest players.

Ahead of last week’s trade deadline, Washington acquired forward Carl Hagelin and defenseman Nick Jensen, and Sunday’s matinee was their fifth and fourth games, respectively, in the Capitals’ lineup. They have looked more at ease with each one, and before this matchup against one of Hagelin’s former teams, Reirden promoted him to the third line with center Lars Eller and right wing Brett Connolly. That decision paid off on the trio’s first shift, when Hagelin scored his first goal with the Capitals at 2:03. As he skated toward the net, he attempted a pass to his left, but the puck hit defenseman Libor Hajek’s skates and rebounded to Hagelin, who punched it past Georgiev and into a half-open net.

Although Hagelin was added primarily for his speed, both on the penalty kill and on the forecheck at even strength, Washington also expected him to have more success offensively in its system. He had just two goals and six assists in 38 games with Pittsburgh and Los Angeles this season, and his last goal before Sunday had come Jan. 17. Hagelin later flashed his ability on the Capitals’ first penalty kill: His aggressiveness created a turnover and forced Rangers defenseman Tony ­DeAngelo to take a hooking penalty to prevent a shorthanded breakaway.

“Since coming here, I’ve gotten some good looks every game,” Hagelin said. “As long as you’re creating chances, you know it’s going to go in sooner or later, and that’s what happened today.”

Like Hagelin, Jensen’s best asset is his skating, and that’s what helped Washington take a lead at 10:02. Joining the attack on a rush, Jensen sped to the net to screen Georgiev as winger Andre Burakovsky beat the goaltender with a wrister from the left faceoff circle. Burakovsky has three goals and six assists in his past 13 games.

The Capitals carried play in the second period with 20 shots on goal, but they weren’t able to capitalize on numerous chances. Instead, the Rangers tied the score at 14:20. After the rebound of a DeAngelo shot bounced into the slot, Burakovsky and Rangers forward Filip Chytil both reached for it, but it was Chytil who was able to corral the puck and set up Pavel Buchnevich’s equalizer. On a power play in the final minute of the period, Ovechkin fired three shots within 33 seconds from his sweet spot in the left faceoff circle, but Georgiev stopped all of them.

Then, on a power play late in the third period, Georgiev again stymied Ovechkin, just barely catching his blistering slap shot with his armpit to keep the score tied and force overtime. He made one last save on Ovechkin on a breakaway in the three-on-three extra period, denying him his 46th goal of the season.

Georgiev’s final stop of Ovechkin was more creative — as well as ultimately illegal — and ironically it handed the Capitals a victory.

“It’s a crazy way to win,” said Capitals forward T.J. Oshie, who also scored in the shootout. “But if he doesn’t throw it, you’ve got to imagine a guy like ‘O’ is putting that in the back of the net. It’s a crazy way to win, but we’ll take it.”