Stamkos made it 3-1 at 10:03 of the third period.
"Everybody is like, 'Holy cow, you lose a game' … or the world's caving in," Lightning coach Jon Cooper said. "I look back at our last two losses. Scoring chances are nearly 2-to-1 (in Tampa Bay's favor), and we've had some pretty good zone time and we've done some good things. We just got beat. There have been some times this year that we probably have not played as well as the other team and won some games."
The Lightning kept up the pressure in the offensive zone, but Rinne made seven saves after Stamkos' goal.
"I thought we had a lot of chances. Their goalie played well," Lightning forward Anthony Cirelli said. "That's a good team over there. We were pushing it until the end there. We've just got to be a little bit better."
Mattias Ekholm made it 4-1 with an empty-net goal with 20 seconds remaining.
Rinne was credited with the second assist on Jarnkrok's goal.
"It's very impressive the way [Rinne] goes about his business," Predators coach John Hynes said. "The mental intensity you have to have every game to be the starting goal is impressive. It's so valuable to have him in and around our team, especially when you have a lot of young guys in the lineup.
"Here you have a guy, his jersey is going to be retired, he's won a Vezina Trophy (voted as the best goalie in the NHL) ... the way he competes. He's a special person. He's going to have a legacy with the Predators."