The hat trick was Keller's second in the NHL. His first came in a 5-4 overtime win against the Philadelphia Flyers on Dec. 11.
"It's nice to see some go in," said Keller, who had two points (one goal, one assist) in his previous 10 games. "It's a long season and you're going to go through tough times, and maybe you don't get the bounces you deserve, but something I've learned is not getting frustrated and sticking with it."
Dylan Guenther also scored, Nick Schmaltz had two assists, and Karel Vejmelka made 35 saves for the Coyotes (15-27-5), who were shut out in their previous two games and won for just the second time in their past 13 (2-11-0).
Phil Kessel scored for the Golden Knights (29-17-2), who have lost four of five. Logan Thompson made 19 saves after playing in a 6-2 win against the Washington Capitals on Saturday.
"We haven't been at our best, and we need to find some consistency in our game and capitalize on our opportunities and play well defensively," Vegas defenseman Brayden McNabb said. "We've got some learning to do. We're in a bit of a funk right now."