Seguin scored at 15:54 of the second for a 4-2 lead. His line with Benn and Radulov combined for seven points (three goals, four assists), 16 shots on goal, and was plus-7.
"It was pretty impressive," Stars coach Jim Montgomery said. "They drove play all the time, and they wanted more ice time. A couple times [Jamie] was banging his stick and looking at me. They wanted it. They felt it, and they were playing well."
Dickinson made it 5-2 at 1:57 of the third period with a slap shot from the slot.
"I go back to it all the time, I think him and Roope [Hintz] and the deep run they had in the Calder Cup Playoffs last year (with Texas) has toughened them up, they relish these games now, they know how to execute," Montgomery said. "You see them have poise, chips in the [defensive] zone, and everything. So, I mean, it's fun to watch those young players blossom."
Turris got Nashville within 5-3 at 2:25 of the third when a pass banked in off Stars defenseman Jamie Oleksiak.
"We've just got to be better, myself included," Rinne said. "It's a huge game on Monday obviously, with our backs against the wall and not the situation we wanted. But you've got to give some credit to Dallas. They're playing well and right now. I feel like they have taken advantage of our mistakes. It's tough right now."