Alex Ovechkin beats Eddie Lack for the game-winning goal in overtime. (Jonathan Newton/The Washington Post)

As soon as Justin Williams’s stick blade tipped the puck up and over Carolina Hurricanes goaltender Eddie Lack, Verizon Center roared with a little extra enthusiasm, understanding the rarity of such a goal by the Washington Capitals. It was the first goal of Tuesday night’s game, and it was the first time the Capitals scored first in nearly two weeks.

They got the last goal, too. Alex Ovechkin scored the overtime winner, snapping a five-game goal-less drought and a two-game losing streak for the Capitals. They beat the Hurricanes, 2-1, clinching a playoff berth with 105 points through 69 games. The Capitals became the first team to punch their postseason ticket.

“We talked about it before the game,” Williams said. “We know where we’re at and we knew the stats. Something we’re very proud of, our record so far. We’ve earned everything we’ve had so far.”

After making 25 saves, goaltender Braden Holtby set a franchise record with his 42nd win of the season. With 13 games left, he has a chance to eclipse Martin Brodeur’s NHL record of 48.

“Obviously it shows the season we’re having here as a team,” Holtby said of his milestone. “That’s good. It shows consistency in what we’re doing.”

Braden Holtby sets a new franchise record with his 42nd win of the season. With 13 games left, he has a chance to eclipse Martin Brodeur’s NHL record of 48. (Jonathan Newton/The Washington Post)

Ovechkin thought he had the game-winner on a shot 10 seconds before his goal. But the Capitals maintained possession after Lack made a save. With Ovechkin backpedaling from the goal line and Evgeny Kuznetsov behind the net, Kuznetsov passed the puck through Hurricanes defenseman Noah Hanifin to Ovechkin. The goal was reviewed immediately, and at first glance the play appeared to be offside, but it was eventually ruled a good goal.

A positive result was only fitting after an early change of pace by the Capitals. Ovechkin said he thought it was the team’s best start to a game in its past 10 or 15, a post or a crossbar denying the Capitals several times.

“Especially in our first period, we showed what we can do to start the game and set up our game,” Holtby said. “You look at it as we only scored two goals with the overtime goal, but we could’ve had quite a few more — just the posts and the tough shots we threw on net in traffic just didn’t go our way, but we stuck with it and that shows that we played a committed game.”

Washington was rewarded for its strong first frame in the second period. Less than two minutes into it, Jason Chimera flicked a puck from the wall and to the crease, where Williams had been left all alone. Williams tipped it up and in 1 minute 30 seconds into the period, and with that score, a wave of relief reverberated through the arena.

Washington had entered Tuesday having allowed the first goal in five straight games, never playing with the lead in any of them. The opponent had scored first in 13 of the Capitals’ previous 15 games, and before Tuesday, Washington was 29-2-0 when scoring first.

“I think sometimes if you just keep talking about it, talking about it and talking about it, then it becomes a problem,” Williams said. “Then you can get it in your head and all sorts of other things. I’m kind of sick of talking about it, but it’s a stat, it’s there and it’s ugly. We got time to rectify that, and I know we will.”

Washington’s first in-game lead since its game against Toronto on March 2 didn’t last long. At the 10:50 mark of the second period, Jordan Staal muscled his way through the offensive zone and his shot ricocheted off Holtby’s pad. With the rebound at his feet, Dmitry Orlov swung his stick to clear the puck but whiffed, and Staal’s second swat at it got past Holtby.

A scoreless third period sent the game to overtime, ensuring the Capitals earned at least a point. That was enough to clinch a playoff spot, their eighth berth in the past nine seasons . But after back-to-back losses in Los Angeles and San Jose , a win was more important to the team than the formality of an assured postseason berth that has long been a foregone conclusion.

Tuesday’s game was a step in the right direction toward eliminating some recent weaknesses, and securing the playoff berth was an added bonus.

“It’s certainly unexpected with this many games left,” Williams said. “It’s a tribute to how we’ve played and we’re proud of where we sit, but not proud enough to rest on our laurels. We’re pushing forward, and you’ll see how good we can be.”