Next up, the franchise's most meaningful regular-season game in years.
Cousins scored a power-play goal early in the third period and the Coyotes boosted their playoff chances Tuesday night, snapping a five-game losing streak with a 1-0 win over the Chicago Blackhawks.
Kuemper made his 18th consecutive start and stopped 31 shots for his fourth shutout of the season. Arizona, which was 0-3-2 in its previous five games, most of those on a recent road trip, has won nine of 11 at home.
The Coyotes moved into a tie with Colorado for the second wild card in the West at 81 points -- though the Avalanche have a game in hand. They host Vegas on Wednesday before a critical head-to-head matchup with Arizona in Denver on Friday.
"Friday night's the most important game in the last what, I don't know how many years. This is something that we're looking forward to," Coyotes coach Rick Tocchet said. "We're having trouble scoring goals. We know that, and sometimes you have to win 1-0 and we did."
The Blackhawks, losers in three of four, were unable to gain ground on any of the four wild-card contenders in front of them in the standings. They remained at 76 points with six games left.
Corey Crawford had 27 saves.
"That one hurts. We needed that one," coach Jeremy Colliton said. "We could have used a little extra urgency earlier on. We weren't bad, but obviously, they score on the power play and we don't. That's the game."
It was the first of three consecutive games for Arizona against wild-card contenders, with Colorado and a Sunday home game against the Minnesota Wild still to come this week.
"It's fun. This is the time of year you want to be playing in, so it's fun to be a part of," Kuemper said. "We're all enjoying it and just have to keep pushing."
The first two periods were scoreless, and the second featured only 12 shots on goal. Chicago got a power-play chance at 11:55 when Clayton Keller was whistled for interference, but Kuemper stopped shots by Alex DeBrincat and Patrick Kane to help the Coyotes kill the penalty.
Lawson Crouse's stick work and hustle drew a penalty on Brent Seabrook for tripping at 4:35 of the third, and the Coyotes got the goal they needed from Cousins at 5:40.
Oliver Ekman-Larsson was credited with the assist, passing to Cousins for a shot that Crawford saved before Cousins put in the rebound for his seventh goal of the season.
"Going down the stretch here every game and every point is crucial for us, so it was nice to help contribute," Cousins said.
The Blackhawks had a few chances to draw even but couldn't get the puck past Kuemper. One opportunity came from former Coyotes player Brendan Perlini with 9:35 to go, which Kuemper somehow turned away with a glove save.
Crouse drew a late penalty with 1:47 left to give Arizona a man advantage. Crawford was pulled for the final 63 seconds, but the Coyotes ran out the clock.
"We had some good chances late there to tie it up but just kind of snake-bitten a little bit," Crawford said. "We did a lot of good things. We've shown we can play in those tight games, but we've just got to try and find a way to win that."
The game featured several players on each side who were facing their former teams: Niklas Hjalmarsson, Richard Panik, Jordan Oesterle and Vinnie Hinostroza for Arizona, and Connor Murphy, Perlini and Dylan Strome for Chicago. ... Hinostroza grabbed Blackhawks captain Jonathan Toews in a scuffle in front of the Chicago net early in the second period, but no penalties were called. ... Mario Kempe, Conor Garland and Ilya Lyubushkin were healthy scratches for the Coyotes.
Chicago: At the San Jose Sharks on Thursday night.
Arizona: At the Colorado Avalanche on Friday night.
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Cousins nets lone goal in Coyotes' shutout win
Nick Cousins scores the game's only goal as the Coyotes top the Blackhawks 1-0.