Bernier spent his first five seasons with Los Angeles before coming to the Maple Leafs this year and he led them to their fourth victory in their first five games of the season.
It was the seventh shutout of his career.
The game was scoreless until Phil Kessel put a slap shot past Pekka Rinne with 6:19 remaining in the second period. James van Riemsdyk boosted Toronto's lead to 2-0 in the final seconds of the middle stanza, after which Tyler Bozak and Joffrey Lupul produced third-period goals.
Rinne gave up the four goals on 26 shots.
This was the ninth time Bernier has faced Nashville in his career and he has won eight of those games.