Maple Leafs winger Zach Hyman entered the zone along the right boards and threw a pass to Mitchell Marner, who appeared to redirect the puck at Rinne.
Rinne made a pad save on the redirection but gave Tavares a wide-open net on a rebound chance. Tavares lined up a wrister and quickly fired the shot at the goal. Rinne sprawled across the crease and made a remarkable blocker save to deny the scoring chance.
The puck floated in the air for a second, allowing Hyman to re-enter the play and chop at Rinne in an effort to push the puck across the goal line. Rinne held the puck out of the net to preserve the Predators' 1-0 lead in the third period.
Nashville defeated the Maple Leafs 3-0 at Bridgestone Arena. Rinne made 22 saves and recorded his fourth shutout of the season. He has a 26-18-3 record with a 2.46 goals-against average and .915 save percentage this season.
The Predators originally drafted Rinne in the eighth round of the 2004 NHL Draft. He has a 337-186-69 record with a 2.38 goals-against average and .918 save percentage. He has 55 shutouts in his career.
Nashville jumped to fourth place in the Western Conference standings after the win. The Predators lead the Vegas Golden Knights by two points and trail the Winnipeg Jets by one point for third.
Rinne and the Predators play the Pittsburgh Penguins on Thursday night.