The Warriors, who had lost 14 of their previous 16 games, rallied from a 16-point deficit in the fourth quarter to force overtime.
Golden State sent the game to overtime when Vladimir Radmanovic hit a game tying three pointer at the buzzer to cap the furious comeback.
Reggie Williams scored 24 points, Dorell Wright had 17 and David Lee added 15 points and 12 rebounds for the Warriors.
Beno Udrih scored a career-high 34 points and Carl Landry had 22 points and 10 rebounds for the Kings. Sacramento has lost six straight and 20 of 22 games.
The Warriors will try to capitalize on the emotional win, and string together a couple of victories, when they host Portland on Christmas night.