The Predators are on a season-high three-game winning streak. Dallas lost for the second time in two nights.
With the Stars on the power play, Brad Richards sent a wrist shot on goal from the left point. Nashville goaltender Pekka Rinne stopped that shot, but Ott was able to pounce on the rebound and beat Rinne on the stick side.
James Neal also assisted on Ott's goal, giving him a point in a career-high six consecutive games.
Ott returned to the Stars' lineup after serving a two-game suspension for a low hit he delivered to St. Louis defenseman Carlo Colaiacovo on Oct. 24.
"We thought that we were really taking the play to them so there was really no doubt in our minds that this game was ours for the taking," Sullivan said.
Nashville took its first lead at 10:59 when Hornqvist picked up a loose puck in the Dallas crease and put a wrist shot underneath the crossbar for his third of the season.
"For the first time in 10 games, I got it right on my stick," Hornqvist said. "It was nice to get a goal again, and if we can keep playing like that we are going to have success the whole year."
Klein put the Predators in front 4-2 at 11:42 with a slap shot through traffic from the right point.
"If you look at all of the goals, there is one common theme that there was someone right in front of the net," Nashville coach Barry Trotz said. "Goals are hard to come by, you have to go to the hard places, and guys did."
Rinne made 27 saves to record his fourth consecutive win. Alex Auld turned aside 29 shots in the loss.
"Both teams had some pretty quality chances, but overall our game has been improving over the last week or so," Rinne said.
Auld felt his team was in good position going into the third period with a 2-1 lead.
"They came out with a lot of sustained pressure, and they scored three hardworking goals," Auld said. "I would have liked to come up with some saves to hold the team in it, but I wasn't able to do that tonight."
This was the third meeting between the teams this season. They won't play each other again until they finish the season series on March 23 in Nashville. ... Dallas G Marty Turco missed his second consecutive game because of flulike symptoms. ... The Predators have scored a power-play goal in three consecutive games for the first time this season. ... Nashville RW Martin Erat missed his second straight game because of a lower body injury.