David Legwand, Jean-Pierre Dumont and Vernon Fiddler added goals for Nashville, which won its eighth straight at home.
Alexei Ponikarovsky and Chad Kilger scored for Toronto, but the Maple Leafs' five-game winning streak was snapped.
Legwand opened the scoring at 14:53 of the first period with his career-best 19th goal. Martin Erat intercepted the puck and skated into the slot with Legwand to his left. He passed to Legwand, who fired a one-timer from midway in the slot past goalie Andrew Raycroft high to his glove side.
Less than a minute later, Mats Sundin took a shot from the left circle that bounced off the glove of goalie Tomas Vokoun. Sundin took control of the rebound and skated behind the goal. He moved the puck to Ponikarovsky, who scored from the right side with Vokoun out of position.
Sullivan gave Nashville a 2-1 lead, scoring from low in the left circle with a one-timer over Raycroft's right pad at 6:23.
Dumont scored on a power-play at 10:09 of the third.
Kilger cut the Predators' lead to 3-2 at 16:13 when he caught Vokoun out of position and scored from in front.
Fiddler sealed the win, scoring an empty-net goal with 31 seconds left.
Notes: Legwand's previous high was 18 goals in the 2003-04 season. . . . Toronto played in Nashville for only the second time since the Predators joined the NHL in 1989. . . . The Predators are 29-7-1 when scoring first. Nashville's Jason Arnott has a point in eight of nine games. Sullivan has 15 points (six goals, nine assists) in 12 games.