Tyler Seguin or Jamie Benn was not among them. Each player had an assist.
Colton Sceviour, Trevor Daley and Ryan Garbutt each had a goal and an assist.
Alex Goligoski had three assists, tying his career high.
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."
Stars goalie Kari Lehtonen allowed three goals on 28 shots.
Pekka Rinne had 22 saves.
After Nashville pulled within 5-3 in the third period on Eric Nystrom's goal, Valeri Nichushkin and Cody Eakin scored 9 seconds apart for a 7-3 edge.
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."
NOTES: The last time seven Stars scored in the same game was 5 years ago. ... Garbutt's first-period goal was his third in two games and his 15th this season. Seguin and Benn are the only Stars with more than 15. ... Seguin had an assist, stretching his consecutive-game scoring streak to 11 games (seven goals, 11 assists). Benn's assist gave him 20 points (eight goals, 12 assists) in his past 16. ... Daley's seventh goal pulled the 10-year veteran within one of his career-high eight in 2010-11. ... The Stars' victory evened the teams' season series at 2-2, with the home team winning each game. The series concludes with the Predators visiting Dallas April 8. ... Shea Weber played in his 600th game. ... Calle Jarnkrok, who assisted on Del Zotto's goal, has one point in each of his first five NHL games (one goal, four assists). ... Before the game, Dallas center Chris Mueller was reassigned to Texas of the American Hockey League. ... On Military Night, Stars players bought 500 tickets and fans donated 500 for active and retired service people. Dallas wore camouflage sweaters for the pregame skate.