The Kings overcame an 18-point deficit to win for the third time in a row, led by Zach LaVine's 43 points and DeMar DeRozan's 37.
With one victory over the Dallas Mavericks, they are still in ninth place in the Western Conference.
Teams that place seventh through tenth advance to the play-in competition the following week.
With four games left in the regular season, the Phoenix Suns, in 11th place, are the only team that can defeat the Kings.
Seventh faces tenth, and eighth faces ninth in the play-ins; the winners advance to the playoffs.
The Miami Heat defeated the already-dead Philadelphia 76ers 117-105 at home, securing a play-in spot in the Eastern Conference after the team's 12th straight loss.
The Miami Heat defeated the already-dead Philadelphia 76ers 117-105 at home, securing a play-in spot in the Eastern Conference after the team's 12th straight loss.