Alex Ovechkin celebrates his third-period goal. (John McDonnell/The Washington Post)

Coach Dale Hunter said it before the puck dropped on the opening faceoff Sunday afternoon: Every set of points is “huge” for the Washington Capitals in the waning days of the regular season.

That fact is omnipresent for the players as they work to ensure themselves a playoff berth. And by dispatching the struggling Minnesota Wild, 3-0, at Verizon Center, they aided the cause.

“Every guy in the room is paying attention to what is going on around the league right now,” Mike Knuble said. “We showed up today for a game that was a must-win and we won it, so we leave here happy.”

Goaltending prospect Braden Holtby earned his first NHL shutout of the season with 28 saves and Alex Ovechkin extended his recent scoring streak with a pair of points, including his ninth goal in seven games.

The victory over Minnesota, which has lost eight of its past 11 outings, gives the Capitals 84 points and pushes them back into the eighth and final playoff spot in the Eastern Conference. The Buffalo Sabres, who visit Washington on Tuesday in a key showdown, have 84 points as well but slide to ninth with fewer regulation and overtime wins than the Capitals (30 to 36).

Washington received some assistance that keeps the Southeast Division lead — and the guaranteed playoff spot that comes with it — in reach. The Florida Panthers fell, 3-2, in a shootout to the Islanders and now hold a three-point lead on Washington, but they do have a game in hand.

But it was a sluggish start to the first and only meeting of the year with the Wild. To keep the game scoreless early required several strong saves from Holtby, including a series of three point-blank stops during a short-handed flurry of chances for Minnesota.

“If I get the opportunity, I want to play hard and win games,” said Holtby, who is 2-0-1 since he was recalled March 18. “Obviously this time of year, with the way the standings are it doesn’t matter who is in goal; it doesn’t matter the reasons. We need wins and we got one tonight.”

Streaking into the offensive zone on a two-on-one rush, Alexander Semin set up Jason Chimera for a back-door tap-in that made it 1-0 on the Capitals’ 10th shot of the game — with 10 minutes 9 seconds gone in the middle frame.

Chimera’s tally, his 19th of the season for a new career high, sparked the Capitals as a whole. They began to establish greater possession and control over the flow of the game and received a lucky break when Minnesota defenseman Clayton Stoner was called for delay of game, when in fact his clearing attempt went off Knuble’s stick before soaring over the glass.

On that ill-begotten power play, the first highlight was perhaps Ovechkin’s best defensive play of the season. With the Wild on a short-handed two-on-one, Ovechkin hustled back into the defensive zone to slide and block a shot by Mikko Koivu. That play thwarted a chance for Minnesota to tie the score and potentially alter the course of the contest — it also brought rousing cheers of “Ovi! Ovi!” from the sellout home crowd.

“It was a great slide, it was like he was playing D all his life,” Hunter said. “It was a great play by him — you know it could have been a difference changer there.”

When the play went back up ice, Ovechkin helped set up Washington’s second goal with a pass to Troy Brouwer on the right-side boards. Brouwer put a centering pass on Mathieu Perreault’s stick for a 2-0 lead 15:15 into the second.

Through 40 minutes, Ovechkin had made one of his most memorable plays of the season, earned a secondary assist on a goal and seen 18:48 of ice time — only three seconds fewer than he played the entire game on Friday in a 4-3 overtime loss to Winnipeg.

Hunter opted to use seven defensemen against the Wild and thus double-shifted Ovechkin for the duration of the contest. In fact, when the star left wing walked into the dressing room he saw his name written on two forward lines instead of one.

He wanted to live up to the challenge of having that responsibility, and in the third period he added another flourish. Ovechkin ripped a snap shot past goaltender Matt Hackett to make it 3-0 and send the crowd into a chorus of chants for him once again. Safe to say, Ovechkin didn’t disappoint.

“When you have that kind of opportunity, you can’t mess up with it,” Ovechkin said. “First period was pretty hard I play almost every second [on] two power plays, full power plays. I just get right away in the game, which is good for me. How I said, I probably play like that two years ago.”

Capitals notes: Joel Ward missed a second consecutive game with a lower-body injury after blocking a shot on Thursday in Philadelphia. . . .

Jeff Halpern was a healthy scratch.