Brayden McNabb had a goal and two assists, Evgenii Dadonov had a goal and an assist, and Robin Lehner made 29 saves for Vegas (40-29-4), which has won six of seven.
"We did a lot of good things," Golden Knights coach Peter DeBoer said. "I loved our start to get the early lead. I thought they pushed back a little in the first. I thought we regrouped between the first and second. I loved our second period. We really grabbed control with how we played even though it wasn't on the scoreboard, and that set up the third."
The Golden Knights moved into a tie with the Dallas Stars for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"We know we have a chance, and we know we kind of control our own destiny," McNabb said. "Tonight was good. We got the two points. Took care of business, but we've got a big road trip coming up. So it's almost like last game, where you have to flush this one and be ready for the next one."
Karel Vejmelka made 33 saves for Arizona (22-44-5), which has lost three in a row (outscored 16-3).
"We knew it would be tough. They played extremely well, so a lot of credit to them," Coyotes coach Andre Tourigny said. "It was really tough for us to sustain possession and make a few plays in a row on the puck. That's one of the best performances from an opponent we've had."
Zach Whitecloud gave Vegas a 1-0 lead at 6:23 of the first period, shooting over Vejmelka's left shoulder from a sharp angle below the right circle.
Pacioretty scored 17 seconds later to make it 2-0 when he finished a shot five-hole from in front.
Barrett Hayton cut it to 2-1 at 10:17 when he one-timed a pass from Michael Carcone on a 2-on-1, but Dadonov scored 38 seconds into the second period on a breakaway to make it 3-1.