Andrei Vasilevskiy made 27 saves and came within 2:00 of his first shutout of the season, and Steven Stamkos scored for the Lightning (15-11-3), who lost to the New York Islanders 5-1 on Monday.
"It was a great effort," Killorn said. "It was a game where we seemed like we played pretty consistent all the way through. I'm really happy with the way we played once we got the lead. It didn't seem like we sat back at all. It seemed like we even elevated our game a little bit more. On a back to back like that when we're traveling, pretty impressed with the way the guys played."
WATCH: [All Lightning vs. Panthers highlights]
Sergei Bobrovsky made 46 saves for the Panthers (15-10-5), who won three of the first four games of their nine-game homestand.
Tampa Bay outshot Florida 48-28, including 34-15 in the final two periods. The 48 shots matched Tampa Bay's season high and were the most allowed by Florida.
"It's one of those nights where you're trying to get something going," Panthers coach Joel Quenneville said. "We didn't have much, whether it was pace or possession. They played it like it was one of the biggest games of the year for them. It was a good measuring stick for us to meet that type of challenge. It was a most important game. It's a learning curve, and we have to be better and expect a much better performance from our team. We have to match that emotion."
Stamkos gave Tampa Bay a 1-0 lead at 6:42 of the first period with his fourth goal in three games. After taking a pass from Killorn, he scored from the crease with a backhand-to-forehand deke.
