Nikita Kucherov had a goal and an assist, Brayden Point scored, and Andrei Vasilevskiy made 26 saves for the Lightning (34-11-6), who have won four straight.
Tampa Bay was playing in its first outdoor game.
"Yes, it's one of 82, but this was a little bit bigger than that," Lightning coach Jon Cooper said. "If you're trying to sell the game in a town that's really bought into hockey, no better way to do it. For me to look back on this, I'll just have warm feelings. It's icing on the cake that we pulled it out."
Tanner Jeannot and Filip Forsberg each scored a power-play goal, and Juuse Saros made 30 saves for the Predators (30-19-4), who have lost five of their past seven games.
Nashville was playing in its second outdoor game. It lost 4-2 to the Dallas Stars in the 2020 NHL Winter Classic at Cotton Bowl Stadium in Dallas.
The announced attendance was 68,619, a sellout and the seventh-largest crowd in NHL history. It was the League's 34th outdoor game since 2003.
"It was great. It was fun," Forsberg said. "Obviously, the fans showed up for both teams. It was an awesome atmosphere. The conditions were great, too. The weather was perfect. The ice was good. Great experience overall, except for the result."
Stamkos made it 3-1 at 11:31 of the third period, beating Saros with a one-timer from low in the left circle off a diagonal pass from Cal Foote. It was Stamkos' 25th goal of the season.
Forsberg scored 58 seconds later to cut it to 3-2.
Nashville had six more shots on goal and another six that the Lightning blocked in the final 7:31, including three shots and six attempts in the final minute.
"I trust those boys that are out there at the end of the game to get it done. They've proven it time and time again," Predators forward Colton Sissons said. "They had a little scramble in front there and I thought might have squeaked one in, but it didn't go our way."