Coyotes goaltender Adin Hill didn’t know he was starting until five minutes prior to his arrival at Gila River Arena. But by the end of the night, the 21-year-old had his first NHL win under his belt.

Once staked to a three-goal lead in the game, the Coyotes allowed two third-period goals to the Los Angeles Kings to send the game to overtime. After a would-be Kings goal in the extra period was waved off, Arizona prevailed in the shootout to notch a 4-3 victory on Tuesday.

The Coyotes are now 5-1-1 in March and 11-3-2 in their past 16 games. They also moved out of the NHL basement, notching their 57th point to move ahead of Buffalo (56). By only managing one point on Tuesday, Los Angeles now holds just a two-point cushion for the third playoff spot in the Pacific Division.

For interim coach John MacLean, who is assuming Coyotes’ head-coaching duties while Rick Tocchet is away on a leave of absence, his first game at the helm was a wild one.

“There was really not a lot going on in that game, right?” MacLean joked. “I mean, a lot of credit goes to the guys. They were focused in and they wanted to win. We talked about it this morning and they know what (Tocchet) is going through. And he wants the guys to accept that responsibility on themselves and I thought they did that tonight.”

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Coyotes interim coach John MacLean breaks down his team’s shootout win over the Kings on Tuesday.

The Coyotes got on the board first when rookie Clayton Keller scored his 19th goal of the season at 5:08 of the first period.

Winger Richard Panik reversed the play around the back of the net and center Derek Stepan raced to the loose puck to keep it in the offensive zone. Stepan found Keller breaking to the right wing circle, and the 19-year-old collected the pass and put one through the five-hole of Kings goaltender Jack Campbell.

The goal gave Keller 50 points on the season, the third-most in Coyotes rookie history. He is now just four points behind Peter Mueller (54), who set the team record during the 2007-08 season.

Arizona made it a 2-0 game when forward Nick Cousins threw a puck on net that squirted by Campbell to give the winger his 11th goal of the season at 15:43 of the first period.

With forward Max Domi tying up Kings defenseman Drew Doughty in front of the net, Cousins’ diagonal shot seemed to ricochet off Doughty’s skate and into the net to give the Coyotes a 2-0 advantage as play moved to the second period.

Coyotes center Christian Dvorak scored at 10:13 of the second period to give Arizona a three-goal advantage. Domi delivered a backhand pass to set up the score.

The Kings usurped the momentum just 27 seconds later.

Kings forward Tanner Pearson scored at 10:40 of the middle frame to make it a two-goal game entering the third period. Los Angeles continued their late-game push and winger Jeff Carter scored twice in the third period to send the game to overtime.

“I don’t know if anything really flipped the script,” MacLean said. “I thought guys played really well and I thought we were dumping the puck deep. LA is a pretty good hockey club and they’re fighting for their lives there. They made a couple plays but I didn’t think they were overwhelming us in our own zone. I liked the response from our guys.”

Off a shot by Carter, Doughty then appeared to score early in overtime but goaltender interference was eventually called upon review. The puck went off Doughty’s skate and into the net, but referees determined that goaltender Adin Hill was interfered with.

“I was pretty confident,” Hill said of whether he thought the goal would be overturned. “I was just hoping, ‘Please don’t count.’ ”

After the goal was waved off, the game went to a shootout where Keller and defenseman Alex Goligoski scored for the Coyotes. Hill stopped four of five shots to notch his first career NHL win.

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Coyotes goaltender Adin Hill reflects on his first NHL win in a shootout against the Kings on Tuesday.

For Hill, who was recalled on an emergency basis on March 6, Tuesday marked his first NHL start since Oct. 26.

“It’s exhilarating,” said Hill, who made 34 saves. “It’s something you grow up every day dreaming as a child. To come here and do it is great. Now, I want more.”

Hill was filling in for an ill Darcy Kuemper, who missed the team’s morning skate on Tuesday and was still not feeling well enough to start by game time — although MacLean said he was available as a backup.

“(Kuemper) needed the morning and we weren’t sure,” MacLean said. “We were hoping he would feel better, but he didn’t. He was available and he was here to be the backup. There was no sense bringing him out in the cold if he’s not feeling 100 percent. But if we needed him, he was ready to go in.”

Hill said he prepared just like he would for any other game — until he received a text from goaltending coach Corey Schwab on his way to the rink.

Schwab also had a hand in the Coyotes’ shootout strategy, as MacLean revealed it was the goaltending coach who suggested that Goligoski give it a go in the fifth round. His reasoning was that Alex and his wife, Amanda, welcomed their second child last week.

“We talk about that all the time,” MacLean said of the shootout strategy. “The first two (shooters) were pretty much scripted. … When you go 3-4-5, it’s a little bit of a crapshoot. Goose is one of the leaders and he’s done a tremendous job. That’s how the process went behind the bench. There’s not a great science to it, but it was effective tonight.”

Goligoski said he was just trying to mirror the move that Keller successfully used on Campbell.

“(Keller) made a great move on his,” Goligoski said. “So I was trying to go down and sell that, and then hopefully freeze him to make an extra move and slide it in. … I’ve never tried it in a shootout before.”

Den’s digest

The score: Coyotes 4, Kings 3.

The streak: W2.

The record: 23-35-11, 8th in Pacific.

The 82-game pace: 27-42-13.

The player: Clayton Keller.

The moment: Alex Goligoski’s winning goal in the fifth round of the shootout.

The number: 50 — With a point on Tuesday, Keller reached the 50-point plateau in his rookie campaign. He is still just 19 years old.

The quote: “Some goalies are gamers and you see them raise to another level. He’s a big kid and I liked his cockiness with how he played the game. I thought he was very confident and especially in the shootout. I think that’s something he can build on. He’s still got some work to do but it’s nice that he got his first win.” — Coyotes interim coach John MacLean on Hill’s first career NHL win.

View from the press box: After the Coyotes blew a three-goal lead, it was hard to envision the team coming away with both points against a hungry Kings team on Tuesday. But they found a way.

Song of the night: “Over The Hills And Far Away” by Led Zeppelin.

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