The Penguins are three wins away from hoisting the Stanley Cup for the second straight year.
Pittsburgh blew a 3-0 lead before recovering to notch a 5-3 win over the Predators in Game One of the Stanley Cup Final.
Jake Guentzel snapped a 3-all tie with 3:17 left in the third.
Nick Bonino scored during a three-goal first period and added an empty-netter for the Pens, who host Game Two of the best-of-seven set on Wednesday.
Ryan Ellis, Colton Sissons and Frederick Gaudreau had the goals for Nashville.