Frank Vatrano scored, and Sergei Bobrovsky made 22 saves for the Panthers (8-2-2).
It was Bobrovsky's first loss in regulation this season (5-1-1). He allowed six goals for the second time in four starts, including a 6-5 overtime loss to the Nashville Predators on Feb. 4.
"We just didn't come to play tonight for the full 60 minutes," Florida defenseman MacKenzie Weegar said. "We were in there for a bit, then the second period came. They just kept taking it to us. We were expecting a big push, and they're the Stanley Cup champions for a reason. We just weren't ready for it. Plain and simple, we didn't have the compete tonight. We look for a big bounce back the next game."
Tampa Bay played a second consecutive game without forward Steven Stamkos, who missed the game Thursday with a lower-body injury and was placed on the NHL COVID-19 protocol list Friday. Tampa Bay also was without forward Anthony Cirelli, who is week to week with an upper-body injury he sustained midway through the third period Thursday.
"We've got some key players out of the lineup that take up a lot of minutes, and guys have to step into their spots, and I thought the guys did an exceptional job," Lightning coach Jon Cooper said. "Guys were moved up the lineup and they delivered. We need depth to be able to weather the storm and those guys did just that, and it's the reason why we won."
Johnson scored the Lightning's final two goals of the second period. His first came on a one-timer on a feed from Smith at 12:58 for a 3-0 lead, and the second on a backhand at 19:48 when he got a loose puck in traffic at the side of the net to make it 4-0.
Florida outshot Tampa Bay 11-4 in a the first period, with the Panthers failing to score on a four-minute power play after Victor Hedman was called for a high-sticking double minor against Aaron Ekblad at 9:33.
"It was huge," Cooper said. "And just the way we did it too. I don't think they had anything brewing for three-quarters of it, and then one stretch we got out there we're a little tired. But to get us through that, we didn't want to be chasing the game again, and when we did break down [Vasilevskiy] was there. But that was a huge kill."
Ondrej Palat gave Tampa Bay a 1-0 lead at 4:11 of the second period with a power-play goal on a one-timer from the right circle. Mathieu Joseph made it 2-0 at 5:32 on a breakaway after blocking a shot just inside the Tampa Bay blue line.