Capitals left win Andre Burakovsky beats Coyotes goaltender Adin Hill for the decisive goal in Thursday’s 4-2 Washington win. (Ross D. Franklin/Associated Press)

After each game, Andre Burakovsky rates his own play, and while scoring might have been the way he measured success a year ago, that’s not the only thing he concerns himself with anymore. His production has been uninspiring this season, especially by his past standards, but Burakovsky has tried to focus more on his total game, and that’s where he’s been most encouraged of late.

But with Burakovsky promoted to the Capitals’ top line for Thursday night’s game against the Arizona Coyotes, he was unhappy with his play. His defensive-zone turnover had led to the first goal of the game, and he continued to struggle. With Washington down two top-six forwards because of injury, Coach Todd Reirden showed his belief in Burakovsky by putting him beside center Nicklas Backstrom and captain Alex Ovechkin, and that belief was tested as he kept him in that role during a game Burakovsky acknowledged was a “tough one” for him.

That decision was rewarded with 4:42 left in the third period, when Burakovsky flashed the offensive skill that’s been missing at times this season. He sped up the ice before unfurling a shot from the left faceoff circle to score the game-winning goal. Ovechkin’s empty-netter in the closing moments sealed the 4-2 win, the Capitals’ first regulation win in Gila River Arena since the 2005-06 season, when Ovechkin was a rookie. It also snapped a two-game losing streak.

“I wasn’t really there today,” Burakovsky said. “Puck was bouncing and got away from me all of the time. Obviously, I did a mistake on their first goal. . . . This game is funny. You’re playing good and some nights you have 1,000 chances and you can’t score. And some nights, you’re struggling hard and seem to get one.”

The Capitals haven’t had their full roster available all season, and their depleted lineup took another hit going into Thursday night’s game with forward Tom Wilson ruled out because of a concussion. A blindside hit from Vegas Golden Knights forward Ryan Reaves on Tuesday caused Wilson’s helmet to come off, and he hit his head on the ice as he fell to the ground. Wilson was suspended the first 16 games of the season, and his return to Washington’s top line helped lift the team back atop the Metropolitan Division standings. He’d scored eight goals with six assists in his first 11 games.

Forward T.J. Oshie, who also has a concussion, missed his 10th game Thursday, and that left the Capitals without their two top right wings. Despite entering the game with just four goals and three assists in 28 games, Burakovsky got the bump up, and just 4:46 into the game, Burakovsky’s defensive-zone turnover led to Christian Fischer scoring the game’s first goal.

“He wasn’t happy with his play on that first goal-against, and I wasn’t either,” Reirden said. “But you have to believe in your players and put them in situations to succeed. I moved him in and out a little bit as the game went on, but I wanted him out there at the end, and he’s able to convert a huge goal for him and for our team. It was a really good moment.”

Burakovsky was Washington’s first-round pick in 2013, drafted to be a scoring winger after piling up points his whole life. But that came harder at the NHL level, and in part because he’s had hand injuries the past two seasons, his production has declined. The stress of not scoring often had Burakovsky angry with himself, and his play away from the puck would suffer if he was in a scoring slump. But after consulting a sports psychologist over the summer, Burakovsky has tried to be more positive with his self-evalutations.

“I’m not drifting away from the game as much as I did maybe two years ago,” he said. “Even if I haven’t produced as many points as people expect or I expect from myself, I still think my game has been way better overall than in the past couple of years, so obviously that’s a good sign. If you look at my play in the [defensive] zone and the way I’m handling the puck, it’s definitely an improvement. I’m not worrying about putting up points here. As long as we’re doing good as a team, to be honest, I don’t care.”

Thursday’s game was the reversal of that: a poor showing overall that was ultimately saved with a goal. Four of his five goals this season have come in the past 12 games.

“Obviously, playing with those guys, it’s going to be more ice time than I’ve been getting here in the past this season, so I’m trying to take advantage of it,” Burakovsky said. “I don’t think I really did much today to help [Backstrom] and Ovi out there. I’m just going to focus on the next one and put this one behind me.”

After the Coyotes took a 1-0 lead into first intermission, the Capitals responded 5:27 into the second period with Jakub Vrana’s third goal in the past two games — and two of those goals have come via assists from Brett Connolly, ratcheting up his total to 13, which is one more than he had all of last season. As Washington’s top-six corps has dealt with injuries, Connolly and Vrana have been the two most productive wingers behind Ovechkin. Both have taken on more ice time as a result, skating on a second line with center Evgeny Kuznetsov.

Arizona’s Lawson Crouse made it 2-1 less than two minutes later, but on his 32nd birthday, Washington defenseman Matt Niskanen scored the tying goal 16 minutes into the second period when his shot from the right faceoff circle deflected off Coyotes defenseman Jakob Chychrun in front.

“That was a gift for sure,” Niskanen joked. “Not much of a shot.”

Considering the Capitals’ injury woes of late, they’ll take any good fortune they can get. Thursday’s win keeps them in first place in the Metropolitan Division.

“It’s an opportunity for somebody to either move up the lineup or get into the lineup, and we’re just trying to take advantage,” Niskanen said. “No excuses. Go out there, play the game hard and try to win. The guys that are changing spots or getting a chance in the lineup are doing a pretty good job for us.”