De’Aaron Fox scored 38 points, including 28 in the final quarter, and Malik Monk 32 off the bench in the Kings’ first play-off game in 17 years.
The seven-match series continues at the same venue on Monday.
James leads lakers into play-offs in thriller
The Philadelphia 76ers, Boston Celtics and New York Knicks won their opening games in the Eastern Conference play-offs.
Joel Embiid scored 26 points and James Harden contributed 23 and 13 assists as hosts Philadelphia beat the Brooklyn Nets 121-101 thanks to 21 three-pointers, a franchise record in the play-offs.
Two days after having five stitches removed from a finger on his shooting hand, Jaylen Brown scored 29 points and made 12 rebounds to help the Celtics beat the Atlanta Hawks 112-99 in Boston.
Brown, who is from Atlanta, missed the Celtics’ final two regular-season games after cutting himself while picking up a piece of glass at home.
The Knicks won 101-97 at the Cleveland Cavaliers despite letting slip a 10-point lead in the fourth quarter.