Nashville has won back-to-back games, while the Maple Leafs have dropped three straight and five out of six.
It was a 1-1 game when Suter put a wrist shot past Ben Scrivens with 7:18 to go in the second period.
Erat scored the only goal in the first period, but John-Michael Liles briefly tied it in the second with a power-play goal. Erat also tallied 2:05 into the third on a slap shot and Matt Halischuk produced an empty-net goal with 23 seconds to play.
Pekka Rinne won his 10th game of the season, one off the league lead, by stopping 38 shots. Scrivens made 18 saves.