Adin Hill made 30 saves for the Coyotes (25-17-4), who lost for the first time in five games.
"We put ourselves in a hole and we had too many guys with their B-game," Coyotes forward Derek Stepan said. "This is one of the best teams in the League. If you're not sharp and executing, they are going to make your night really difficult."
Alex Killorn made it 1-0 at 15:06 of the first period when he jammed in a loose puck off the rebound of Maroon's shot.
Mikhail Sergachev extended the lead to 2-0 at 18:24 when his centering pass deflected in off Coyotes defenseman Jordan Oesterle.
"I honestly didn't think we were bad, I think we were fine, until that three minutes, two crucial plays," Arizona coach Rick Tocchet said after his team lost by at least four goals for the first time this season. "We lose our coverage in front, it's not a good goal. Then we had three guys caught, they had a 4-on-2, it's a bad goal. So, it's 2-0.
"Then we started kind of unraveling. We had some guys, I didn't like their energy level. I don't know why."
Kucherov made it 3-0 at 6:15 of the second period, then made it 4-0 at 8:52 on a one-timer from a sharp angle off a pass from Stamkos, who gathered a rebound in front.