Late in overtime, David Legwand picked up a loose puck in the Winnipeg zone and sent a pass to Smith at the left faceoff dot, where he hammered a one-timer past Jets goaltender Ondrej Pavelec, who had 30 saves.
"I felt Leggy made a good play, he put it on a tee," Smith said. "The emphasis in this room is to shoot the puck and we did a good job of creating chances. I was the finishing touch right there."
Tied at 1 entering the third period, Mike Fisher sent a shot on goal from the right boards. Hornqvist picked up the rebound in the high slot and fired a shot by Pavelec for his fourth goal of the season at 6:04 of the third.
"Our second goal was a controlled breakout sort of setting," Nashville coach Barry Trotz said. "We got Fisher wide and he hammered it at the net. We got two whacks at it, and the second one went in the net and that is shooting to create."
Hornqvist leads the Predators in goals this season.
With 3:01 left in the third, Wheeler skated through the slot and converted the long rebound off a Zach Bogosian shot.
"I think we did a lot of good things," Wheeler said. "We came out and had a really good start. In the first 10 minutes, we were all over them, kind of let them off the hook a little bit, and they took a little bit of the momentum away from us."
Weber scored the game's first goal at 15:53 of the opening period.
With the Predators on the power play, Seth Jones broke up a short-handed scoring opportunity by Winnipeg's Evander Kane. Nashville went the other way and Weber beat Pavelec with a wrist shot to the stick side from the high slot.
The Jets got even at 13:49 of the second on Peluso's first career goal.
From the right side, Peluso carried the puck behind the Nashville goal and his wraparound attempt just crossed the goal line before Carter Hutton's stick knocked the puck back out of the crease.
The play was initially ruled no goal on the ice, but a quick video review showed that the puck did cross the goal line completely.
"The game for me was played in pockets of consistency and inconsistency," Winnipeg coach Claude Noel said.
"We started out the first 10 minutes; I thought we were really solid then. From there we weren't able to sustain some of the stuff we were doing. The biggest task for our team is to be consistent through the whole 60 minutes."
Carter Hutton won his second game against the Jets in the past week. He led Nashville to a 3-1 victory Sunday night in Winnipeg, his first career win.
He will be busy over the course of the next month, as Rinne, Nashville's top goaltender, underwent arthroscopic surgery Thursday afternoon to clear up an infection in his left hip, the same hip he had surgery on following the conclusion of last season.
"I am just taking it day-by-day, shot-by-shot, period-by-period, kind of slow things down," Hutton said. "You look at the big picture, it can be a bit overwhelming, especially I've only played a couple of games."
Thursday's procedure will keep Rinne out of the Nashville lineup for at least four weeks.
Weber holds the Nashville record for power-play goals scored with 51. ... Nashville is 5-0-1 when scoring first this season. ... The Jets began a four-game road trip, all against fellow Central Division opponents. ... Winnipeg has not scored a power-play goal in its past six games.