Rinne, who earned his second shutout of the season on his 36th birthday, signed a two-year, $10 million contract earlier Saturday that will keep him in Nashville through the 2020-21 season.
"It's a pretty cool day," Rinne said. "I came in in the morning and signed a two-year deal. Extension, birthday, it's been an awesome day. Huge win. I'm just very happy, so proud that I can stay with this organization that gave me a chance a long time ago and still have that opportunity to chase my dream. I'm very, very fortunate."
WATCH: [All Bruins vs. Predators highlights]
Roman Josi scored for the Predators (11-3-0), who have won three straight and lead the NHL with 22 points.
"That's a really good team over there," Josi said. "I thought we played really well for 60 minutes. We didn't give them that many chances. Obviously, we'd like to play better on the power play and capitalize on a couple chances, but I thought as a team we played really well."