The game, aired nationally on NBC, drew a 9.4 rating. The previous record, a 7.2 rating, had come in Game 6 of the 2015 Stanley Cup Playoffs against the Chicago Blackhawks in the first round.
Nashville leads the best-of-7 series 2-1. Game 4 is at Bridgestone Arena on Tuesday (9:30 p.m. ET; NBCSN, SN, TVA Sports).
The Predators fans will be out in full force again, clad in gold, screaming their lungs out, delivering standing ovations during every television timeout for Game 4, holding down their part of the covenant with the team.
"They have been awesome, they never disappoint," Nashville defenseman Mattias Ekholm said. "They give us energy. They really are the seventh man out there."
Defenseman P.K. Subban arrived in Nashville on June 29, part of a trade that sent former captain Shea Weber to the Montreal Canadiens, who play in one of the most fervent hockey cities in the world.
Subban spent the first six full seasons of his NHL career in Montreal. He, perhaps more than anyone, can judge how high the bar has been set here.
"Nashville is second to no one in terms of the game entertainment and presentation on the ice," Subban said. "This organization, in terms of how they do business; it's been first class. I'm just really excited to be a part of it."