The Golden Knights took a 5-0 lead when Chandler Stephenson scored at 4:10 of the second period, but the Coyotes scored three straight goals, including two in 58 seconds in the third period.
Reilly Smith scored twice, and Robin Lehner made 22 saves for Vegas (26-11-2), which had 13 players score at least one point.
"[The first period] won the game for us," Smith said. "The first four, five shifts, we generated 10-15 shots and a couple goals, and I think that changed the game."
Nick Schmaltz had a goal and an assist, and Phil Kessel had three assists for Arizona (19-17-5), which has lost two games in a row after winning three straight. Adin Hill allowed five goals on 32 shots through the second period and was replaced to start the third by Ivan Prosvetov, who made three saves.
"We weren't ready to play," Schmaltz said. "They're a great team, and that's what's going to happen. It's definitely embarrassing."
The Golden Knights scored four goals in the first period in a span of 5:41.
Jonathan Marchessault scored at 3:03 to make it 1-0, the first power-play goal in 19 attempts in seven games for Vegas.
"We've not been clicking with [the power play]," Marchessault said. "We need to be a force. There's no excuse for that group to not have a successful power play. It was a good first goal, and we can get confidence from that."