Hill started with Antti Raanta and Darcy Kuemper each out with a lower-body injury. The 23-year-old had played two games in relief this season.
"A little bit nervous, but once you get to the rink and you get into your routine before the game, all that kind of disappears and you're just playing the game you love," Hill said. "I felt good. I guess I saw a lot of pucks. The guys did a great job locking it down for me for the first game. For my first start of the year, they played a great game, and special teams seemed to be the key to the win."
WATCH: [All Coyotes vs. Panthers highlights]
Taylor Hall had a goal and an assist for the Coyotes (25-16-4), who matched their season-best winning streak with their fourth in a row.
"These last four games, you're seeing every line is kind of playing the way that they want to play and a lot of guys are chipping in," Hall said. "That's great for the team's confidence."
Chris Driedger made 32 saves in his second consecutive start ahead of Sergei Bobrovsky for the Panthers (22-16-5), who have alternated wins and regulation losses in their past six games.
"We need to just kind of dig deep here," Florida forward Noel Acciari said. "We can't be going back and forth. We need to string together three, four wins in a row and kind of separate ourselves a little bit from the bottom of our (Atlantic) Division so we can have a little bit of a cushion. But right now it's not going right for us, but I have faith in this locker room and we all know what we need to do."
Christian Dvorak gave Arizona a 1-0 lead at 10:20 of the second period when he tipped in Hall's wrist shot from the right circle. The goal was confirmed after it was reviewed for a high stick.