Kings’ Coyote-ugly win over Arizona a thing of beauty to Andy Andreoff

He smiled after the puck got past Arizona goalie Mike Smith late in the second period.

It lingered. He kept smiling on the bench and was still smiling at the end of second period. You can guess that 23-year-old Andy Andreoff was still smiling on the drive home after the Kings’ game against the Coyotes.

There’s nothing quite so heartwarming as a hockey player’s first NHL goal, the fulfillment of years of hard work and promise. Not only did rookie center Andreoff score his first NHL goal (and first point) but it was the game-winner for the Kings in a 1-0 victory over Arizona on Monday night at Staples Center. For Kings goalie Jonathan Quick, it was his sixth shutout of the season and second in less than a week. He faced 25 shots.

Andreoff called it a “dream come true.”

“It’s been a long year, so I’m glad I finally got it,” said Andreoff, a third-round draft pick in 2011. “Noles [Jordan Nolan] made a great play to me for a tap-in. . . . I’ll take one off my shin pad, off my butt. It doesn’t matter, as long as it goes in.”

Bigger picture: The win lifted the Kings into the final wild-card playoff spot in the Western Conference, past idle Winnipeg. The Jets host the San Jose Sharks on Tuesday, and the Calgary Flames, third in the Pacific Division, are in action, too.

All that helped overshadow the fact that Monday’s offering was one of the more, um, methodical games of the season. At least that’s the polite way to put it. Arizona went 0 for 2 on the power play and the Kings have killed off 41 of the last 43 penalties against them.

The lottery-bound Coyotes, now 1-14-1 in their last 16 games, are a shadow of the team that lost to the Kings in the Western Conference finals in 2012.

“It’s a land of opportunity when you’re a team that’s not in the playoff race,” said Kings Coach Darryl Sutter at Monday’s morning skate.

That land of opportunity could apply to the likes of rookie center Nick Shore and Andreoff. Andreoff’s place in the lineup — this time — came after center Jarret Stoll was injured Thursday in Vancouver.

This was the first time Andreoff has played in back-to-back games since mid-January. He nearly scored Saturday, hitting the post against Nashville, and finally broke through in his 15th NHL game, beating Smith in close, off a terrific pass from a poised, patient Nolan. Defenseman Brayden McNabb had the second assist.

“I kind of blacked out. I couldn’t really hear anything,” Andreoff said. “I was just shocked. . . . I was very relieved to finally get it. I saw [Nolan] battling in the corner and he’s a good playmaker. He would either put it in or give it to me for a backdoor tap-in.”

Said Sutter: “Not many players get a chance of playing in the NHL or scoring goals. Good for him. Hopefully, he’s got lots of game-winners left in him.”

Earlier, Sutter had gone over his approach regarding less-experienced players, explaining his version of the land of opportunity.

“If they’re going to play — even though some of them have been here for awhile — if they’re going to play serious minutes for us, then we better win and they better produce. They better have a role that they embrace.”

Sutter tweaked the lines at the start, putting Dustin Brown with center Anze Kopitar and Marian Gaborik, and taking Trevor Lewis off the Kopitar line and put him with center Jeff Carter and Tyler Toffoli.

“We’ve got guys that haven’t scored in 10 or 11 or 12 or 13, 14, 15 games, or whatever it is,” Sutter said. “. . . We’ll leave Jeff and Tyler together and leave Kopi and Gabby together and let everybody else see where they can play.”

lisa.dillman@latimes.com

Twitter: @reallisa