It was the fifth win in seven games for the Predators, who are 8-1-2 in their last 11 against the Jets.
Nashville won in what will be the first of a long line of games it will play without goaltender Pekka Rinne.
The team announced earlier in the day that Rinne will undergo surgery to repair a hip infection and will be out for at least a month.
Carter Hutton, starting his second game of the season and the third of his career, stopped 34-of-36 shots as Rinne's replacement.
Nashville twice took the lead on goals by Shea Weber in the first period and Patric Hornqvist early in the third. Winnipeg rallied on each occasion with Anthony Peluso and Blake Wheeler scoring the goals.
Ondrej Pavelec took the loss with 30 saves. The Jets have dropped three straight.