Going into the game, Seguin had 75 points and Benn 69. Dallas' third-highest scorer was Goligoski, with 33.
Vernon Fiddler, whose first-period goal was his fifth this season, said: "It's nice to get some depth scoring. At the end of the day, we've got to continue to do that. The big guns need some help with that, and it takes a little bit of pressure off of them."
Nichushkin's unassisted goal went off Predators defenseman Shea Weber's stick.
"We tipped two in our own net," Weber said. "They got one off the skate, and then they scored off the rush. They got a little bit of everything, and it just wasn't good enough for us."
That's why Nashville coach Barry Trotz didn't consider pulling Rinne.
"Not really, even when they got six and seven. Six and seven were deflected. There was nothing you could do about it."
Stars coach Lindy Ruff, who preaches putting pucks on the net, was pleased about the four goals that deflected off teammates' sticks or bodies.
"We got some good breaks. We had a couple put in by their defensemen. We got enough pucks going to the net, and got rewarded for it."
Goals by Garbutt and Fiddler gave the Stars a 2-0 lead after one period.
Sceviour, Alex Chiasson and Daley scored in the second period that ended with a 5-2 advantage for Dallas.
The Predators' Patric Hornqvist and Michael Del Zotto also scored in the second.
The victory improved Dallas' playoff hopes. The Stars have 81 points -- three behind Phoenix, which has the Western Conference's last playoff position.
The Stars have nine games remaining, including a game Saturday at St. Louis. Phoenix has eight to play.
The game started well for the Stars against Nashville, which was coming off a 6-1 win over Buffalo on Thursday.
"They looked fresh," Trotz said. "They jumped on us. I don't know how many pucks we just got it to the red line and just turned it over and they transitioned on us, and it's hard to play that way. You're spending your energy in the wrong area."
Garbutt gave Dallas a 1-0 lead when he tipped Antoine Roussel's pass from the right corner past Rinne.
The Stars took a 2-0 lead on a 2-on-1 rush at 14:05 of the first. As a defender slid to the ice attempting to block a shot, Sceviour passed across to Fiddler on the right side, and he drilled a snap shot into the net.
Dallas outshot the Predators 9-5 in the first period.
Nashville's best chance to score came on the only shot during the power play, when Craig Smith's shot from the top of the left circle went off Lehtonen's pads.
Goligoski and Daley, Friday's starting defensive pair, each finished with plus-5 ratings.
Ruff said: "That's a good night when you're plus-5 on the score sheet. I think you've seen by ice times these last 30-40 games how much we think of that pair and how much difference they can make. They made some real good plays for us."