Curry sank a pair of free throws with 8.6 seconds left for a two-point Golden State lead.
Sacramento's Isaiah Thomas then drove the length of the floor for an attempted equalizing layup, but Bogut blocked it into the backboard and collected the rebound as the horn sounded.
Curry also recorded 10 assists and Klay Thompson fired in eight 3-pointers en route to 28 points for the Warriors.
Bogut finished with six points, 12 rebounds and three blocks.
The Kings got 24 points from DeMarcus Cousins.
Marcus Thornton contributed 21 and Thomas finished with 19.