Phil Kessel was honored with a pregame ceremony for playing his 1,000th consecutive game.
"It was neat," Kessel said. "Obviously, 1,000 games in a row is a lot. I don't know how I did it, but it's a good thing."
Clayton Keller scored, and Karel Vejmelka made 35 saves for Arizona (6-9-1), which has lost three in a row.
"We look at our last couple of games where we play really well for a long time, but we cannot close the deal or get the big goal," Coyotes coach Andre Tourigny said. ""We missed Grade A opportunities. We had other plays where we needed to be quicker with our shot to get the goalie in motion, stuff like that. There's a lot of work to do offensively for us."
Pietrangelo gave the Golden Knights a 1-0 lead at 12:21 of the second period, scoring with a one-timer from the point on a power play.
"Sometimes you got to attack, keep it simple and shoot the puck," Pietrangelo said. "I didn't know if it was going to go in or not. Sometimes you got to shoot and hope for the best."
William Carrier scored 31 seconds into the third period to make it 2-0. He curled around the right circle while holding off Coyotes forward Matias Maccelli, cut toward the slot, and shot short side on Vejmelka.
"We knew that the next goal was going to be real important," Carrier said. "We're trying to get something going. … Obviously, it was a big goal. Big play by [Keegan Kolesar] in front, gave me a little bit of room and I took the room."
Mark Stone extended the lead to 3-0 at 5:53 when he batted the puck into the net after Pietrangelo's one-timer deflected off the stick of Coyotes defenseman Josh Brown.