Kuemper, making his second straight start because No. 1 goalie Antti Raanta has flu-like symptoms, was coming off a 35-save performance in a 4-1 victory at the Columbus Blue Jackets on Tuesday.
"He's really confident back there. He looks big in net right now," defenseman Alex Goligoski said. "When a goalie looks big, he's playing confident. He's been great for us."
Goligoski put the Coyotes ahead 1-0 with a backhand shot from the slot 43 seconds into the second period. It was the first goal by the Coyotes in three home games and the first by an Arizona defenseman this season.
The Canucks (6-5-0) tied it 1-1 less than two minutes later when Darren Archibald, playing his first NHL game this season, deflected Troy Stecher's shot from the point past Kuemper at 2:23.
"I thought we played good hockey, I thought we were pushing," Vancouver coach Travis Green said. "Even after the [Keller] goal, we made a strong push …. for a back-to-back game, and playing a team that's playing well."
Canucks forward Sven Baertschi (concussion) and defensemen Alexander Edler (knee) and Chris Tanev (hip) did not play after they were injured Wednesday in a 3-2 shootout win at the Vegas Golden Knights, their fifth victory in seven games. Forwards Elias Pettersson (concussion) and Brock Boeser (groin) remained out.
"To get guys coming in and out of the lineup early in the season, it is tough," forward Bo Horvat said. "But at the same time, we've got to find a way to win games. It was tough to not get two points here."
The Coyotes have scored 16 goals in five games since scoring three in their first four games.
"We were gripping [the sticks] a little bit tight when we weren't scoring, and it was the difference in some games," Goligoski said. "We dug ourselves a hole when we were 1-4. You can't get behind early in the season, we know that all too well."
The Coyotes started 0-10-1 in 2017-18 and never got close to .500 after that.
"There was urgency in that we had a chance tonight to get close to .500," coach Rick Tocchet said. "Was this a must-win? In our eyes, this was a game we needed. I liked that while we were sloppy in the first two periods, our players dug in in the third period."