Los Angeles became only the fourth team in NHL history to win a playoff series after dropping the first three games with a 5-1 win over the San Jose Sharks.
The Kings, who joined the 1942 Toronto Maple Leafs, the '75 New York Islanders and '10 Philadelphia Flyers with the ultimate comebacks, advance to meet the Anaheim Ducks in an all-Southern California second-round match-up that will start on Saturday.
Elsewhere, Minnesota right-winger Nino Niederreiter scored in 5:02 of overtime and the Wild rallied late and beat the Colorado Avalanche 5-4 in Game Seven of their first-round playoff series.
It was Niederreiter's second goal of the game, and it came on a 2-on-1 break right after the Avalanche had a chance at the other end.
The New York Rangers beat the Philadelphia Flyers 2-1 in Game Seven at Madison Square Garden to win their first-round playoff series.
The Rangers, who are now 6-0 in Game Sevens on home ice, will face Pittsburgh in the next round. The Penguins beat the Columbus Blue Jackets in the first round.