"We've won 10 of our last 11," Golden Knights captain Mark Stone said. "I joked with the guys (that) we're not the Harlem Globetrotters, we can't win them all."
Adin Hill, in his first start since April 11, made 25 saves in his third NHL shutout for Arizona (22-24-5), which gained ground in the Honda West Division playoff race after losing four of its previous five games and nine of 11.
"We were disciplined," Hill said. "We had only two penalties, we kept their shots to the outside, we just made simple plays and cleared the puck. It was great to watch. We played a simple game, but we kept doing exactly what we wanted."
Robin Lehner made 29 saves for Vegas (35-12-2), which had not lost since April 7.
The Golden Knights lead the Colorado Avalanche by four points for first place in the West; the Avalanche defeated the San Jose Sharks 3-0 on Friday and have one game in hand.
Stone said there might have been an emotional letdown against Arizona following a 5-2 win against Colorado on Wednesday.
"Offensively, we just weren't very good," he said. "They're fighting for their lives, and they've pretty much got to win out, and they brought their best game."
The Coyotes are fifth in the eight-team West, three points behind the St. Louis Blues for the final Stanley Cup Playoff berth from the division but with three fewer games remaining. The Golden Knights, Avalanche and Minnesota Wild have qualified for the playoffs.
John Hayden, Michael Bunting and Christian Fischer scored for Arizona, which lost five of its first six games against Vegas this season.