Capitals forwards Troy Brouwer (20) and Brooks Laich celebrate Brouwer’s go-ahead goal, which stood up as the game-winner. (Jonathan Newton/The Washington Post)

As the Washington Capitals gathered in their dressing room at Verizon Center during the second intermission Saturday night, what had already been an ugly week threatened to continue on. Trailing the Phoenix Coyotes by two, the Capitals were 20 minutes away from losing a fourth straight game when they decided to change their course.

Washington charged back in the third period, recording three goals — by Karl Alzner, Brooks Laich and Troy Brouwer — within a span of 5 minutes 2 seconds to capture a 3-2 win over the Coyotes and snap the three-game losing streak.

Recently acquired goaltender Jaroslav Halak posted 31 saves in his Capitals debut and learned the dramatic ways of his new team. “It was a [heck] of a comeback by our guys,” he said. But it was the outburst of offense, beginning with Alzner’s goal, that ended a morale-stifling scoring drought of 115 minutes 45 seconds that stretched back to the third period at Philadelphia on Wednesday. It also allowed the Capitals to keep pace in the postseason hunt.

Washington sits 10th in the Eastern Conference but is one point back of the final wild-card spot (Detroit, 71 points) and doesn’t own any tiebreakers. With only 17 games left in the regular season, the players have realized time isn’t on their side.

“We were just kind of sick and tired of the way things were going,” Alzner said of the mood before the third period. “Just stop feeling sorry for ourselves. It’s time to get real. [Joel Ward] likes to say sandpaper . . . play gritty and be rough out there. We were just trying to pump ourselves up a little bit more because we haven’t had enough of a spark in the last couple.”

Up until Alzner’s shot from the point at 9:45 of the third period, the Capitals had been steadily foiled and frustrated by Phoenix netminder Mike Smith (30 saves). Smith withstood a furious push in the early stages as Washington came out with a strong start after sluggish first-period outings in each of its past two games.

But while firing six shots in the first 6:40 of play marked progress from failing to record more than eight in the first 40 minutes against either Philadelphia or Boston, the early chances weren’t enough to crack Smith. Each save the Phoenix goalie made seemed to siphon energy from the Capitals, and soon the familiar habits began popping up in their game.

Jack Hillen was checked as he pushed the puck along the boards while several other Capitals were trying to get off for a line change. The puck bounced toward Keith Yandle, who sent a pass up ice to Brandon McMillan, who had both speed and the angle on Mike Green after the defenseman turned the wrong way at the blue line. McMillan snapped a shot past Halak’s stick side to put Phoenix up 1-0 with just 62 seconds remaining in the first.

Then, early in the second, Radim Vrbata outmuscled Dmitry Orlov down low on a power play to swat the puck across the goal line after a shot trickled through Halak’s pads to make it 2-0.

“Sometimes it’s very frustrating the way other teams are playing,” Capitals Coach Adam Oates said. “It’s not going your way, [and their] goalie’s hot, making big saves — easily we could have been up 1-0 in the first period with that power play, easily. We had some great chances, and he stopped them. You’ve just got to wait your turn.”

But the Capitals had life in the third, and once Alzner’s shot floated into the upper left-hand corner of the net, they rolled.

On the next shift, Washington established a cycle, and as Jason Chimera worked away to protect the puck in the left corner he managed to send a forceful centering pass to the slot. Laich, who played after skipping Thursday’s game at Boston and admitted he isn’t 100 percent healthy after aggravating his nagging groin injury on Wednesday, smashed the puck past Smith, making it 2-2 just 32 seconds after Alzner’s goal.

When Coyotes forward David Moss went off for tripping Orlov just more than three minutes later, the opportunity to snatch a win awaited. Brouwer scored a power-play goal on a rebound from a shot by Nicklas Backstrom to give the Capitals a 3-2 lead that they translated into an important pair of points.

“We need points. It’s against a team in a different conference, but we still need points,” Brouwer said. “We know that we’re at a point where our season is on the line every single game, and that should be enough motivation in here and it was tonight.”

Capitals notes: Washington recalled center Casey Wellman from Hershey.