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.
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.
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.
Weber scored the game's first goal at 15:53 of the opening period.
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 Nashville goaltender 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.
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 Pekka 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.
Thursday's procedure will keep Rinne out of the Nashville lineup for at least four weeks.
Notes: 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.