Mike Hoffman and Vincent Trocheck scored, and Bobrovsky made 25 saves in Joel Quenneville's first game as Panthers coach.
"I liked the first 40 minutes, the last 20 were too loose for us and they got some timely goals late in the power plays," Quenneville said. "I thought for the most part we were in pretty good shape and then we didn't have the puck much in the third, which was, you know, in their favor, because they've got a lot of skill and a lot of speed when they do have it."
Palat put the Lightning ahead 3-2 at 9:34 of the third period when he scored off a power-play rebound of a shot redirection by Alex Killorn. Maroon made it 4-2 at 13:51 when he scored on a rebound off a shot by Victor Hedman.
"Just gotta go to the front of the net, good things happen," Maroon said. "Lucky bounce off the boards, but my job is to stay in front of the net and look for dirty second and third opportunities. The boys did a good job of whacking the puck and getting second and third opportunities. I was just there to clean up the trash."
Erik Cernak scored an empty-net goal with 46 seconds remaining to make it 5-2.
Kucherov, the leading scorer in the NHL last season, made it 1-0 at 6:39 of the first period with a one-timer from outside the circle off a feed from Sergachev while the Lightning had a man-advantage from a delayed penalty.
Hoffman tied it 1-1 at 2:35 of the second period after Trocheck dug the puck out of the corner. Shattenkirk made it 2-1 at 10:28.
"For me it was really just getting the puck to the net and hoping for the best," Shattenkirk said. "It seemed to be there most of the night, the shooting lanes ... it was just one of those ones that you kind of look and everyone else starts celebrating before you, so you figure something good happened."
Trocheck tied it 2-2 with a shorthanded goal at 8:49 of the third period.
"This is not a good feeling," Florida captain Aleksander Barkov said. "We had the game in our hands. We played really well but we just couldn't win and we need to learn how to win."
