Sidney Crosby also scored, and Tristan Jarry made 24 saves for the Penguins (30-21-9), who won their third in a row following a four-game losing streak.
"I think we're getting there," Crosby said. "I think we'd still like to limit the chances against and make sure we're not putting ourselves in bad spots just from our own doing, make teams work for their chances if they're going to get them."
Mark Jankowski scored, and Juuse Saros made 31 saves for the Predators (29-23-6), who had won three straight.
"We kind of went toe-to-toe the whole game," Nashville captain Roman Josi said. "It was kind of a back-and-forth game. We had some chances. They had some chances. Just couldn't find a way to win it, but I felt like our effort was good. We played well."
Jankowski, who was recalled from Milwaukee of the American Hockey League earlier Tuesday, gave the Predators a 1-0 lead at 7:01 of the third period. He intercepted an outlet pass by Kris Letang at the top of the circles, skated down the slot and scored backhand-forehand.
"When I got the puck on the turnover there, I looked up and saw I had some time," Jankowski said. "So, I thought I would see what I could do, and just waited out the goalie there."
Crosby tied it 1-1 at 11:00, scoring on a breakaway after receiving a stretch pass from Brock McGinn.
"I see an opening and sometimes guys get time with the puck and other times they don't," Crosby said. "[McGinn] made an unbelievable pass to me. It was flat, right on the tape and I had lots of time to make a play from there."