Tkachuk put Florida ahead at 11:20 of the third with a wrist shot from the left circle after Sam Bennett found him trailing in off the rush.
Seth Jones also scored, and Jacob Markstrom made 19 saves for the Panthers (2-0-2), who concluded a four-game season-opening road trip.
Florida forward Brad Marchand sustained an apparent lower-body injury late in the second period. He was high-sticked by Kings defenseman Brandt Clarke while driving the net, which sent Marchand awkwardly into the right post with 53 seconds remaining in the period.
Marchand was in visible pain while holding his left knee on the ice. He stayed down for a few minutes and was attended to by a trainer before helped off the ice by Brady Tkachuk and Niko Mikkola.
Alex Laferriere scored, and Darcy Kuemper made 26 saves for the Kings (0-2-1), who were playing their home opener.
Laferriere put Los Angeles up 1-0 at 19:00 of the first period. He was at the bottom of the left circle to collect a cross-slot pass from Erik Haula and shoot into an open net.
Jones tied it 1-1 at 3:49 of the second period, cutting toward the net on a rush and beating Kuemper top shelf. The goal came after the Panthers killed a two-man advantage and an extended power play that was caused by Dmitry Kulikov's double minor for high-sticking at 19:43 of the first.
