Mike Ribeiro scored the only goal the visitors needed in the first period but James Neal added another at 7:31 of the third.
Ribeiro, picked up by Nashville (3-0-1) after they missed the playoffs last season, redirected a shot from Seth Jones past Ondrej Pavelec at 16:19 to get things started.
Then Neal, another off-season acquisition, beat Pavelec through traffic with a puck that appeared to glance off a couple of Jets to add some insurance.
The Predators had four power plays and the Jets three, but neither scored. Both teams have struggled with their power play this season and it's not a new issue for Winnipeg, which ranked 25th in the NHL last season.
The Jets (1-3-0) have now gone four games without scoring a power-play goal and the Predators are doing only slightly better with one.
Rinne showed why his absence from the Nashville net was so painful last season, frustrating the Jets' best several times.
Winnipeg put on lots of pressure but the veteran drafted by Nashville in 2004 seemed to anticipate every move. The Jets outshot the Predators 31-27.
Rinne played only 24 games last season due to a hip injury as Nashville missed the playoffs for a second season a row. Coach Barry Trotz was sacked.
Winnipeg's record for home openers fell to 1-3 with the loss.
It was the second time this short season they've been unable to score a goal. The first was in San Jose Oct. 11 when they lost 3-0.
Notes: The Jets (not counting their Atlanta years) are now 2-3-1 in their meetings with the Predators. Olli Jokinen made his first appearance in Winnipeg Friday night in a Nashville uniform after spending two seasons with the Jets.