Erik Gustafsson gave the Blackhawks a 1-0 lead at 6:33 of the first period on a wrist shot through traffic from the point.
"It's good that we're closing the gap," Gustafsson said. "I think our start of the season wasn't that good, but we're trying to figure out how we're supposed to play out there now. I think we're playing more as a team, and we showed that today."
Dominik Kubalik made it 2-0 at 18:04. Predators defenseman Matt Irwin lost the puck to Blackhawks forward Kirby Dach deep in the defensive zone, and Dach fed Kubalik in front.
Brent Seabrook made it 3-0 at 1:51 of the second period on a backhand from beyond the circles.
David Kampf extended the lead to 4-0 lead at 11:39 on a one-timer from the top of the slot.
"I thought it was a good performance, especially the first two periods," Chicago coach Jeremy Colliton said. "Obviously we scored on our chances, and we got some really timely saves too by [Lehner], especially in the first few minutes when they had a bit of a flurry. Scored some timely goals, and obviously the guys have some confidence and had some fun out there."