Foye went 4-of-4 from the free throw line in the extra frame while Al Jefferson contributed 15 points and 12 rebounds for Utah, which racked up its third win in four games.
Paul Millsap, Alec Burks (14 points each) and Derrick Favors (13) also played big roles as the Jazz improved to 18-5 on their home court.
The Kings got 23 points and 10 rebounds from Jason Thompson, but it wasn't enough to prevent them from finishing their six-game road trip with a 1-5 mark.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys