"I'm always hungry," Hawryluk said. "I'm always looking to score, make plays, or help our team win. That's just the way I play."
Jared McCann and Frank Vatrano each had a goal and an assist, and Mike Hoffman and Denis Malgin also scored for Florida (15-14-6), which is 4-1-0 in its past five games after a four-game losing streak (0-3-1). James Reimer made 26 saves.
WATCH: [All Panthers vs. Blackhawks highlights]
The Panthers won their first game of the back-to-back 2-1 at Detroit on Saturday.
"We talked about it before the game, a back-to-back game, the young guys have to be our heartbeat and they did it tonight," Panthers defenseman Keith Yandle said. "Jayce [had] two goals, [McCann] nice goal, [Frank Vatrano] … all the young guys took over tonight and found a way to have fresh legs and get us a big W."
Dylan Strome had a goal and two assists, and Connor Murphy and Alex DeBrincat scored for Chicago (13-20-6), which saw its three-game winning streak end. Cam Ward made 21 saves.
"We were feeling confident," Strome said. "Even after the first period, we were still playing pretty good. Once they get a goal, we let them take the wind out of our sails and let them get too much momentum from that. We really lost momentum, and they gained it.
"[We've] got to find a way to let those plays go and focus. That third and fourth goal really quick killed us. It's unfortunate we couldn't come back."
Murphy gave the Blackhawks a 1-0 lead at 13:23 of the first period on a wrist shot from the right face-off circle. It was his first goal of the season.
Hawryluk's first NHL goal tied it 1-1 at 16:21 of the first. He eluded Carl Dahlstrom and kept the puck when Ward left the crease to play it and scored into an open net.