Nikita Kucherov, Steven Stamkos and Mathieu Joseph each had a goal and an assist, and Andrei Vasilevskiy made 32 saves for the Lightning (27-9-5), who won their fourth straight game.
Cal Petersen allowed five goals on 24 shots for the Kings (20-15-5), who were swept in back-to-back games following a 6-2 defeat at the San Jose Sharks on Monday.
"That's kind of what we expected was going to happen, a kind of back-and-forth kind of game," Kings forward Alex Iafallo said. "But when that happens, you just got to kind of pack it in and take your chances and get better chances. But we'll have to regroup, and we'll be fine."
Hedman gave Tampa Bay a 4-3 lead at 10:43 of the third period on a wrist shot from the high slot. He leads all NHL defensemen with 43 points (nine goals, 34 assists).
"I think he's one of the top five players in the National Hockey League, not just tonight but every night I turn on the TV," Kings coach Todd McLellan said. "Six-foot-six and play like that, and he had a huge impact on the game. Played the most minutes of anybody and played the best out of everybody, so he was good."
It was Hedman's ninth multigoal game, passing Dan Boyle for most by a Lightning defenseman.
Joseph made it 5-3 at 15:20 with a sharp-angle shot on a one-timer from McDonagh and Stamkos scored into an empty net at 17:18 to make it 6-3.
Phillip Danault scored at 19:07 for the 6-4 final.
Hedman scored on a breakaway with a wrist shot in the slot to put the Lightning up 1-0 at 13:17 of the first period. He has seven points (two goals, five assists) during a four-game point streak.
"We want to try and grab the lead, especially in these circumstances," McDonagh said. "We were playing a little conservative. He got a bouncing puck and was able to go on the breakaway."