Killorn had two goals and two assists for the Lightning, who are the No. 3 seed in the Discover Central Division and lead the best-of-7 series. Andrei Vasilevskiy made 39 saves.
Jonathan Huberdeau and Carter Verhaeghe scored for the Panthers, No. 2 seed. Sergei Bobrovsky made nine saves on 14 shots before being replaced in the second period by Chris Driedger, who made 11 saves.
Tampa Bay can win the series in Game 5 at Florida on Monday (8 p.m. ET; CNBC, FX-CA, TVAS, BSFL, BSSUN).
"Just go back home and forget about this one," Panthers captain Aleksander Barkov said. "We played well in their zone, had some shifts in their zone, but they found a way to score goals. That's unacceptable. We have to find a way to eliminate those. Go play in front of our home fans, get excited and play the right way for 60 minutes."
Anthony Cirelli gave Tampa Bay a 1-0 lead at 3:00 of the first period, shooting five-hole on a breakaway. Yanni Gourde pushed the lead to 2-0 with a deflection of a shot from Kucherov at 7:24.
"I just tried to get to the front of the net, tried to screen the goalie," Gourde said. "And I tried to have a step on the side so any rim out I can get to the puck from behind the net. I was fortunate enough to see the puck the whole way and get a stick on it."
Huberdeau cut it to 2-1 at 8:49 with a power-play goal, and Ondrej Palat made it 3-1 at 16:45 when he deflected Erik Cernak's shot.
"You look at this game, and it looked like we were out of it, but I don't think that was the feeling," Panthers defenseman Anton Stralman said. "I don't think we gave up a lot of chances. The ones we did give up were just too good."