Hornqvist gave Nashville a 4-2 lead 5:13 into the third when, on a power play, he skated off the goal line to flip a sharp-angled shot past Panthers goaltender Jacob Markstrom.
Smith broke a 2-2 tie 1:22 into the period. Taking advantage of a Florida line change, a passing play from Shea Weber to Gabriel Bourque resulted in a loose puck in front of Markstrom that Smith converted.
"I just crashed the net," Smith said. "I just went to the net. We've been harping all camp and through the beginning of the season here, going to the net hard. I did that and I was rewarded.
"When you shoot the puck, things happen. Guys want to shoot the puck and that's great. There's a lot of funny goals out there."
Nashville (3-3-0) scored more than three goals for the first time this season, but coach Barry Trotz was not happy.
"It was a frustrating game," Trotz said. "I would probably say that game we were probably the most sloppy we've been in all the games this year; not real detailed, making poor judgment errors all over the ice, just not real sharp tonight. But we found a way to win and that's part of learning to win."
Jonathan Huberdeau, Marcel Goc and Matt Gilroy scored for Florida, which has lost five of six after an opening-night victory against the Dallas Stars. Markstrom made 26 saves.
Florida (2-5-0) hasn't won in Nashville since 1999; the Predators have seven wins and a tie since then.
"We're trying to take out the small mistakes," Panthers coach Kevin Dineen said. "I don't fault the compete level; we've talked about that too much. We had numerous chances with the empty net and their goalie made some big saves.
"We got a 60-minute game. We gave up a bad power-play goal that was a savable goal. We need to start winning these games. We need to win."
Gilroy made it 4-3 with 8:27 remaining when his centering pass was tipped into the Nashville net by backchecking Predators forward David Legwand. It was the first goal scored by a Panthers defenseman this season.
"We had some chances at 4-3," Huberdeau said. "We missed some chances at the end. Markstrom kept us in it. You have to take the positives from this game. We had a good effort. … We had some lines clicking. We just have to be better defensively to help Markstrom."
Goc tied the game 2-2 at 12:30 of the second period. Nashville defenseman Victor Bartley tried to bat the puck, but it wound up on Goc's stick at the post to Rinne's left.
Fisher became the first Predators player to reach two goals this season 42 seconds earlier. Smith created a turnover in the Florida zone and found Fisher wide open racing off the bench on the right-wing side.
Ten Predators had scored the team's first 10 goals of the season. Hornqvist's goal was his second.
Fisher assisted on the opening goal of the game, a blast from Weber at the blue line that buzzed past Markstrom at 9:23 of the first period.
The Panthers scored first in the second period. A hit by Mike Weaver created a turnover that wound up with Scott Gomez heading up the right-wing boards. Trailing the play, Huberdeau entered the offensive zone, took the pass, deked around defenseman Kevin Klein and slid the puck under Rinne at 1:16.
Material from team media and wire services was used in this report