Erik Cole had the goal for Dallas, which has lost three of four.
Cole scored the game's first goal at 18:07 of the opening period when he took possession of the puck behind the Nashville net and skated out front before lifting a backhand over Hutton's right shoulder.
Making his second consecutive start, Hutton improved to 6-3-1 this season.
Nashville closed out the first period with power-play goals from Hornqvist and Legwand just 28 seconds apart.
Dallas got into trouble when Shawn Horcoff took a high-sticking penalty at 18:45 and Brenden Dillon was sent off for delay of game 7 seconds later when his clearing attempt from inside the Stars blue line sailed over the glass.
Hornqvist got Nashville on the scoreboard at 19:02 on the two-man advantage.
From the bottom of the right circle, Legwand found Hornqvist alone in the slot, where he wired a wrist shot high to the stick side of Dallas goalie Kari Lehtonen.
Legwand scored on the 5-on-4 at 19:30 when he collected the rebound of Roman Josi's shot from the left point and put it by Lehtonen for his sixth of the season.
Shea Weber assisted on both of Nashville's first-period goals, giving the team captain 10 points on the power play this season.
Nashville is 11-0-1 when leading after the first period.
Gaustad gave the Predators a two-goal lead at 9:14 of the second, beating Lehtonen with a wrist shot from the left side. The goal came on a delayed penalty to the Stars and with Hutton off for an extra attacker.
Gaustad has four points in his last two games.
NOTES: Dallas D Aaron Rome appeared in his first game of the season. ... Josi has points in three consecutive games. ... Nashville won for just the third time when allowing its opponent to score first.