The Capitals’ Jason Chimera is denied by Maple Leafs goalie James Reimer during the third period. Chimera scored once during a three-goal opening period that helped Washington beat Toronto. (Matt McClain/The Washington Post)

Though the Washington Capitals’ offense has sputtered at times this season, making leads hard to come by and wins even harder to find, their more frustrating habit has been letting leads they do build disintegrate.

On Sunday at Verizon Center, the Capitals erupted for three goals in the first period, then ducked their heads through a furious storm of Toronto shots in the second, somehow emerging into the calm of the third with a one-goal lead. Clinging to two points they couldn’t afford to lose, Washington refused to relent in the final 20 minutes.

The Capitals turned in a solid third period to hold off the Maple Leafs until Troy Brouwer added an empty-netter with less than four seconds remaining to seal a 4-2 win that steadied Washington’s playoff pulse heading into a grueling three-game California swing.

“I thought if anything we could have taken it to them a little bit harder,” defenseman John Carlson said of the third period. “We didn’t sit back on our heels and wait. . . . I thought we did a good job of sealing things down when we needed to.”

As fellow playoff hopefuls bolstered their résumés with big weekends — most notably Metropolitan Division rival Philadelphia, which stole four points from Pittsburgh — that third period loomed large, the difference between being effectively eliminated from contention and staying alive, two points behind the New York Rangers for the final wild-card spot in the Eastern Conference.

Defenseman Karl Alzner said the Capitals’ wins in their past two home games “are massive. They’re games we knew we needed to win before going out on this road trip. . . . A lot of teams have games in hand against us, so we need to do our best to get it back even.”

For the second straight game — a noteworthy streak given the Capitals’ penchant for sluggish beginnings — Washington (32-27-10, 74 points) struck first. On the Capitals’ first power play of the game, Nicklas Backstrom carried the puck at the half board, inching toward the faceoff circle as Marcus Johansson loomed low. Backstrom sent a quick feed to Johansson, who redistributed to Troy Brouwer, who was clear in front of the crease and scored to put the Caps up 1-0.

Not much more than a minute later, Karl Alzner fired on Maple Leafs goaltender James Reimer (29 saves), and the rebound found its way to Joel Ward. He turned around a backhanded shot that slid through the legs of Reimer, off the skate of Jason Chimera at the far post and in.

On Washington’s next power play, Evgeny Kuznetsov — playing at the half-board spot held by Backstrom on the top unit — hit newly acquired forward Dustin Penner, who twirled a backhand pass to Ward in front of the crease. Ward buried it, giving Penner his first Capitals point and Washington its sixth three-goal first period of the year.

“That’s the way you want to start, for sure,” Chimera said. “I think they were a little sluggish to start.”

The Maple Leafs (36-25-8, 80 points) awoke in the second period, following a two-shot, one-goal first period with 20 shots in the second.

Three Washington penalties aided Toronto’s cause, but the Capitals killed all three in a span of seven minutes, making Dion Phaneuf’s seeing-eye flick from the blue line the only goal in a period that looked certain to give Toronto more.

“They’ve got a great power play, and we did a great job, so I thought [the kills] gave us a little life towards the end of the period,” Washington Coach Adam Oates said. “Then we came out and had a very strong third period.”

Though the Capitals didn’t mount many charges in the third, they didn’t allow the Maple Leafs to equalize, either. When Toronto busted through the Caps’ skaters and into space for the types of game-tying scoring chances the home crowd has come to dread, the Caps’ defense recovered. Jaroslav Halak did his part in the third, turning away seven Toronto shots. He finished with 27 saves as he pushed his Capitals record to 3-2 in five consecutive starts.

“We did better things with the puck,” said Chimera, asked about the difference between Sunday’s third period and less successful showings earlier this season. “We got it out when we needed to, guys got it deep when they had to, didn’t take unnecessary chances.”

The Capitals frustrated the Leafs until a Troy Brouwer clearing attempt from deep in his own zone bounced off the boards and toward the empty Toronto net with 3.9 seconds left. Nicklas Backstrom chased the puck the length of the ice but never touched it, selflessly giving Brouwer the goal, Karl Alzner an assist and the Capitals the must-have win.

“That is the best move a person can do and that I’ve ever seen. It sums up the kind of person he is,” Alzner said of Backstrom’s decision not to score.

“We’ll see. That’s definitely something that would be considered that rally-around moment. A good team play.”

Capitals note: Forward Brooks Laich, who missed Sunday’s game because of his lingering groin injury, will not travel with the team on its three-game trip to California, Coach Adam Oates said. Laich will travel to St. Louis to meet with specialist Michael Brunt for the second time in a week. Oates said Laich might undergo a “small procedure” similar to one he had last spring.