Austin Wagner and Drew Doughty scored, and Jonathan Quick made 27 saves for the Kings (16-23-3), who have lost three of four following a four-game winning streak.
"When you play a team like that you know you have to play well or they can make you look bad in your own rink, so our guys were ready cause they knew that could happen," Kings coach Willie Desjardins said.
Kucherov gave the Lightning a 1-0 lead at 6:28 of the first period, scoring for the fifth straight game during a 5-on-3 power play. It was Kucherov's 400th NHL point in 406 career games, becoming the first player from the 2011 NHL Draft to reach the 400-point milestone.
Kucherov extended his point streak to 12 games. He has 27 points (eight goals, 19 assists) during his streak, including 15 assists in his past seven games. It was the seventh consecutive multipoint game for Kucherov, who leads the NHL with 69 points.
"He's dangerous every time he's on the ice, and you give our team a 5-on-3 there at the beginning, you kind of expect Kucher and these guys to put it in the back of the net," Joseph said. "Great job by him, and he's been the leading scorer in the League and it's not for no reason."
Point made it 2-0 at 7:53 during the same two-man advantage. He has 13 points (three goals, 10 assists) during an eight-game point streak.
Callahan extended the lead to 3-0 at 14:05 when he intercepted Jake Muzzin's pass in the neutral zone and scored on a breakaway. Callahan ended a 15-game goalless drought with his first goal since Nov. 23 against the Chicago Blackhawks.
McDonagh scored 25 seconds into the second period to make it 4-0 before Wagner cut it to 4-1 at 7:55. Stamkos extended the lead to 5-1 at 17:05 on the power play.
Joseph made it 6-1 at 10:04 of the third period.
Doughty scored on the power play at 17:36 for the 6-2 final.
