James Neal also scored for Nashville, winners of four of their last five.
Blake Wheeler had the lone Winnipeg goal. The Jets have lost two of three.
With time winding down in the third, Calle Jarnkrok found Smith at the bottom of the left circle, where he beat Winnipeg goaltender for his sixth goal of the season.
Wheeler scored the game's first goal at 6:57 of the second period.
After a turnover in the neutral zone by Nashville's Matt Cullen, Wheeler skated in on the right side and beat Predators goaltender Pekka Rinne with a wrist shot to the glove side.
RInne finished with 21 saves.
Wheeler's eight goals lead the Jets. He has three in his last two games.
After not allowing a short-handed goal against last season, Nashville has allowed two so far this season. The Predators did not record a shot on goal in eight minutes of power play time in the game.
Neal tied the game 1-1 at 15:45 of the second on a one-timer from the high slot off a pass from Mike Ribeiro that beat Pavelec high to the glove side.
That goal came just eight seconds after Ribeiro appeared to have tied the game. The goal was waived off when it was ruled that the puck was played with a high stick.
Pavelec made 27 saves in the game.
Notes: Nashville C Colin Wilson returned to the lineup after missing two games with a lower-body injury. Nashville has allowed the first goal in 12 of 17 games this season. Neal has points in four consecutive games. Winnipeg completes their current five-game road trip Sunday in Minnesota.