Arizona outshot Vegas 53-28, including 28-5 in the second period when Hill made 26 saves.
William Karlsson gave the Golden Knights a 4-3 lead with a goal from the right circle at 18:02 of the third period. Zachary Hayes had two goals, and Michael Amadio had three assists for Vegas.
Barrett Hayton had one goal and two assists, and Jonas Johansson made 24 saves for Arizona.
Hayes gave the Golden Knights a 1-0 lead at 8:53 of the first period and made it 2-0 at 13:57, each on an assist from Amadio. Matias Maccelli cut it to 2-1 at 4:19 of the second period on a rebound at the right post before Hayton tied it 2-2 at 6:01 when the puck deflected off his skate on the rebound of a shot by Dylan Guenther.
Pavel Dorofeyev gave the Golden Knights a 3-2 lead, scoring from the slot off a pass by Sakari Manninen at 12:06 of the third period. Alex Chiasson tied it 3-3 on the power-play at 17:44 with the Coyotes playing 6-on-4 after pulling Johansson.
