Filip Forsberg scored for the Predators to give them a 1-0 lead at 18:08 of the first period on a rebound from a shot by Josi.
"I think we've been more detailed," Forsberg said. "I think the second period today was not that, but I thought the first period was great. We're being a little more, not careful, but we're just taking care of the puck better and it's not hurting us as much."
Viktor Arvidsson gave the Predators a 2-0 lead at 7:53 of the second period on a one-timer on the rush.
"We went out in this game and I think we dominated the first period and went on the offensive attack," Arvidsson said. "It was a great game for us, and we finished it great."
Josi gave the Predators a 3-1 lead at 9:56 of the third period on a wrist shot from the point. It was his 14th goal, the most among NHL defensemen.
Chychrun scored for the Coyotes to make it 3-2 at 10:33 of the third period.
"It's frustrating," Crouse said. "We didn't like our start, but we battled pretty much right until the end. Those are the characteristics that you want to see. Obviously [Raanta] did a [heck] of a job for us back there. He gave us a chance to win the game, and that's really all you can ask for."
Crouse scored for the Coyotes to make it 2-1 at 18:07 of the second period on a backhand shot on the rush.
"We're going to just stick together," Tocchet said. "It's a tough trip here, a lot of air miles. We're going to have three days off and get the guys to reenergize."