Tyler Toffoli scored his eighth goal, and Jonathan Quick stopped 38 shots for the Kings (11-3-2), who lost at home in regulation for the first time (5-1-2). Oscar Fantenberg scored his first career NHL goal in the third period.
Making his first start against the Kings after playing in 53 games for them last season, Budaj made a blocker save on Anze Kopitar's one-timer at 9:11 of the first period that Lightning coach Jon Cooper said changed the game.
"I thought for sure it was in. I think everyone in the building thought it was in," Hedman said.
The stop led to a Kucherov breakaway, where he took a pass from Stamkos and scored on a backhand at 9:27 for his third straight game with a goal.
Killorn scored 34 seconds later to make it 2-0. Hedman scored on a wrist shot after being left alone during a 4-on-3 rush at 10:35 for a 3-0 lead.
The Kings challenged that Brayden Point was offside, but the play stood after a lengthy review and Los Angeles was assessed a delay-of-game penalty. Stamkos then scored his sixth power-play goal at 11:29 for a 4-0 lead off Killorn's backhand pass to set up the one-timer.
"The wheels kind of came off for a little bit there," Kopitar said. "Against a team like that, you know you can't outscore them because they have a lot of firepower."
Toffoli weaved through four defenders and scored at 17:31 of the second period to make it 4-1. Kopitar scored with 47 seconds left but the goal was overturned when the Lightning successfully challenged for goalie interference.
