Rinne made 30 saves for his 15th NHL shutout, Cal O'Reilly scored in the game's first minute, and the Predators held on to beat the Stars 1-0 on Saturday night.
Dallas (5-2) had 22 goals in its first six games, the club's best offensive start since netting 23 in the opening six games of the 1996-97 season. But the Stars couldn't get the puck past Rinne in the opener of a season-high, six-game homestand.
"We looked at it as a big challenge," Predators coach Barry Trotz said. "We knew we were going to need a big goaltending performance out of Pekka, and we got it."
"We played a good road period," Trotz said. "We kept the fans quiet. We said if we were going to win this game, it would have to be 1-0 or 2-1. So it was huge, getting that goal."
Rinne did the rest for the Predators, especially in the second period when Dallas held a 13-5 shots advantage.
The Predators (4-0-3) won their first three games and then dropped three consecutive overtime decisions before getting back on track in their second road game of the season.
"We knew (the Stars) had a good offense and a lot of firepower," Rinne said. "The last three games we lost in overtime, so we said this time, we just needed to get mad."
Lehtonen stopped 23 shots in the matchup of Finnish goaltenders.
The Stars have cleaned up some areas of concern that were somewhat masked by their early success. They've cut down on shots against, and improved on special teams, killing off two Nashville man-advantage situations after entering the game with an NHL-worst penalty kill rate of 64 percent.
"We've won a few games where maybe we shouldn't have," Lehtonen said. "Then this one, we probably should have."
Rinne made a sprawling stop on Loui Eriksson's point-blank attempt on a power play midway through the second period.
Lehtonen denied Sullivan on a breakaway with less than nine minutes left in the second.
"We put a lot of quality scoring chances on net but couldn't find a way," said Dallas' James Neal, who finished with five shots. "I had a few good chances I'd like to have back. But that's how it goes sometimes. It's frustrating, but you've got to stay positive and do what you were doing before. You'll get rewarded."
Notes: LHP Derek Holland of the American League champion Texas Rangers handled the ceremonial opening puck drop. ... Ryan Suter, a member of Nashville's top defensive pairing, missed his second consecutive game because of a lower body injury. The Predators are also without C Matthew Lombardi (concussion) and C Marcel Goc (separated shoulder). ... The Stars had scored at least three goals in each of their first six games. ... Predators RW J.P. Dumont left the game in the third period because of a lower body injury. Trotz said Dumont is day-to-day. ... The Predators opened a stretch of 11 road games over a 14-game span, including Sunday's game at Tampa Bay.