GLENDALE, Ariz. — All it took was one goal on Tuesday night.

Actually, it took more than that. It took Darcy Kuemper’s fourth shutout of the season and a late heroic goal by Nick Cousins, plus some solid defense, a successful penalty kill and a touch of good fortune, in order for the Coyotes to earn what was perhaps their most important win in years.

The Arizona Coyotes (37-33-7) bested the Chicago Blackhawks (33-33-10) on Tuesday night, 1-0, as Kuemper made 31 saves and the game’s lone goal wasn’t scored until 5:40 in the third period.

“We’re having trouble scoring goals and we know that,” head coach Rick Tocchet said. “Sometimes you’ve got to win 1-0 and we did. And that’s something that I’m proud of this team about doing. It took 1-0 to win.”

With the win, the Coyotes’ point total matches that of the Colorado Avalanche, who occupy the second wild card spot in the Western Conference. The tiebreakers aren’t too important yet, since the two teams will play each other in Arizona’s next game; the Coyotes travel to Denver to play the Avs on Friday.

“Friday night’s the most important [Coyotes] game in the last, what, how many years — right?” Tocchet said. “So this is something that we’re looking forward to. This is a big, big game for us on Friday.”

The Coyotes now have just five games remaining, and the next two are against teams that are fellow Western Conference wild card race participants: Colorado and Minnesota. These games — and Tuesday’s win — follow a four-game road trip on which Arizona went 0-3-1.

“We needed a response,” Kuemper said. “Obviously dug a little bit of a hole on the road. We were playing good, just didn’t get the results, so we knew we just had to stick with it. It was playoff-type hockey tonight, for sure, but we got the huge win.”

Tuesday’s win over the Hawks could serve as a good introduction for what’s to come. Indeed, the intensity was playoff-esque, as the Blackhawks were fighting for their lives. Now five points back with six games to go and three teams to leapfrog, Chicago’s playoff chances seem pretty grim.

Friday will only be even more intense as the Avalanche try to keep Arizona at bay.

As for Tuesday’s game, Cousins’ big goal was his seventh of the season and comes after he was scratched for the team’s game on Sunday in Long Island. That goal might’ve been the most important single goal Arizona gets all season.

“It wasn’t the prettiest of games for the fans, maybe,” Cousins said. “But this time of year, you’re not going to find too many high-scoring games. That’s what you saw tonight. You get one power play goal and score and that’s the game, right? That’s what it’s going to take at this time of year and that’s a big one for us.”

Of the Coyotes’ five remaining games to finish the regular season, two are on the road: Friday at Colorado and April 4 (next Thursday) at Vegas. The Coyotes are 18-18-3 on the road this season, which amounts to more road wins than 13 other teams. Arizona is 19-15-4 at home.

“I think we handle the road really well,” Tocchet said. “So I’m not really worried about this team. We know we’re going to have to go to Colorado, we’re going to have to score some goals. And we’ll talk about that in the next couple days.”

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