Clayton Keller and Brad Richardson scored the other goals in Arizona's second straight victory. Schmaltz's two points were his first since being acquired Sunday in a trade with the Chicago Blackhawks.
As the final horn sounded to end the game, the puck was deep in the Nashville zone. Ekman-Larsson skated the length of the ice to retrieve it for his rookie goaltender.
''You are putting a guy in that position and he wasn't nervous at all,'' Coyotes coach Rick Tocchet said of Hill. ''You're playing in a tough building, one of the best teams in the league and he did a nice job.''
Nashville has lost three of four.
''They were faster than us,'' coach Peter Laviolette said. ''They wanted it more. We didn't have enough guys with their hands on the rope pulling it our way. So that's what we got.''
Hill stopped nine shots in the first period, 14 in the second and six in the third.
''I thought of it a bit towards the end of the third,'' Hill said about the shutout. ''But I was trying to focus on the whole game just getting the win.''
Keller scored first at 1:40 of the second period.
Schmaltz carried the puck into the Nashville zone and skated around the left faceoff circle. Near the boards, he found Keller in the slot, where he beat Predators goalie Pekka Rinne with a wrist shot low to the stick side.
''We need to get skating again. We need to work hard for each other,'' Nashville defenseman Mattias Ekholm said. ''Right now it feels (so-so), but the sun will go up tomorrow.''
Schmaltz made it 2-0 with 20.9 seconds remaining in the second.
With the Coyotes on a power play, he beat Rinne with a wrist shot from just above the right faceoff dot off an assist from Ekman-Larsson.
''I just took my ice and tried to pull it and get it through,'' Schmaltz said. ''It was fortunate to go in there. It slipped through the six-hole, I think.''
Ekman-Larsson's six power-play points lead the Coyotes.
Richardson made it 3-0 at 11:23 of the third on a one-timer from the high slot.
Rinne finished with 22 saves.
NOTES: Ekman-Larsson played his 600th career game. ... Arizona is 6-3-1 in its last 10 against Nashville. ... The Predators are 11-4-1 when outshooting their opponent. ... Nashville was shut out for the second time this season.
Coyotes: Host the St. Louis Blues on Saturday.
Predators: Host the Chicago Blackhawks on Saturday.
More AP NHL: https://apnews.com/NHL and https://twitter.com/AP-Sports
Copyright 2018 by AP. Any commercial use or distribution without the express written consent of AP is strictly prohibited.