Cousins went 10-of-15 from the floor and Isaiah Thomas added 26 with eight assists off the bench as the Kings broke a six-game losing streak.
Ben McLemore forced overtime with a 3-pointer at the end of regulation and finished with 15 points.
Gordon Hayward scored 22 points and Trey Burke tallied 19, 10 rebounds and seven assists for the Jazz.
Alec Burks put in 19 points in a reserve role.
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