Thomas made two free throws to cut the Jazz lead to 93-92 with 37.9 seconds remaining. Burke and Burks each converted two free throws apiece in the final 18.2 seconds around Cousin's inside shot before McLemore hit his big 3.
Burke's runner at the regulation buzzer bounced off the back of the iron.
Burke scored five points to spark a 16-0 Jazz run in the fourth quarter that erased Sacramento's nine-point lead. Hayward capped the run with back-to-back jumpers and a free throw to make it 91-84 with 2:59 to play.
Thomas helped the Kings move in front by scoring nine points in the final 3:08 of the third quarter. His third teardrop runner of the surge gave the Kings a 74-70 lead headed into the fourth.
Thomas made another driving bucket and added two free throws and an assist to Patrick Patterson to extend the Kings' advantage to 84-75 with 7:28 remaining in regulation.
The Jazz and the Kings entered the game tied for the fewest wins (4) in the NBA with Milwaukee).
Jefferson, who finished with 13 points, made three 3-pointers in the first half and the Jazz led by as many 10 points.
After the Jazz won three of four, they dropped a close contest to Indiana, but then were blown out by Portland, 130-98, on the road and have now lost three straight.
Meanwhile, the Kings looked like they might end their skid Friday against the Lakers but blew a late lead and lost 106-100.
Four of the defeats in the Kings six-game skid were by a combined 11 points and they looked ready to turn a corner. McLemore followed his career-high 20 points in Los Angeles with 15 points and nine rebounds against the Jazz.
Cousins overcame early foul trouble and was extremely efficient in his 28 minutes of play. The center was 10 of 15 from the field and was the focal point of the Sacramento offense in overtime.
Favors, a potential foil for Cousins who had started all 21 games this season for the Jazz, sat out with a sore lower back.
Cousins committed two fouls in the first minute of the game and Utah's Mike Harris had five fouls before halftime. Harris and Jeremy Evans both fouled out in regulation and Enes Kanter fouled out in overtime. . In the first quarter, the Kings twice intentionally fouled Andris Biedrins, a career 50 percent free throw shooter. Biedrins made 1 of 6 from the line. . Cousins lost his trademark headband late in the fourth quarter on a hard foul by Kanter.
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SALT LAKE CITY, UT - DECEMBER 07: Jason Thompson #34 of the Sacramento Kings drives against Jeremy Evans #40 of...
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