Nicolas Hague, Brendan Brisson and William Karlsson scored, and Logan Thompson made nine saves for Vegas.
Maveric Lamoureux scored, and Connor Ingram made 25 saves for Arizona.
Lamoureux gave the Coyotes a 1-0 lead at 2:58 of the second period when he one-timed a loose puck in the left face-off circle.
Hague tied it 1-1 at 11:35 with a wrist shot from just inside the blue line, and Brisson put Vegas in front 2-1 at 19:45.
Karlsson scored into an empty net with 28 seconds left in the third period for the 3-1 final.
