Paul Millsap added 14, with a key block, step-back jumper and rebound in the extra session for the Jazz, who used an 8-0 fourth-quarter run to take the lead with 2:40 left in regulation.
Utah had a chance to win it in regulation, but big man Al Jefferson shot an air ball 3-pointer at the buzzer.
Jason Thompson led the Kings with a season-high 23 points, and Tyreke Evans added 20 but had a key turnover in overtime.
Former BYU star Jimmer Fredette had just two points, three turnovers, and missed all five shots from the field, finishing with two points in 13 minutes of action.
Sacramento played the second half without leading scorer DeMarcus Cousins, who was ejected for arguing with officials at midcourt during the halftime break.
Cousins started 4 of 4 and finished 5 of 8 with 10 points and six rebounds.
Alec Burks had a season-high 14 points for Utah, including a 19-foot shot on the run that gave Utah a 90-87 lead in overtime.
The Jazz won despite being without point guards Mo Williams and Earl Watson and third-leading scorer Gordon Hayward.
Burks had to step up and he did, making 5 of 7 shots, with four assists, three rebounds and a nasty block.
Utah won despite committing a season-high 22 turnovers that led to 24 Sacramento points.
The Jazz shot 52.8 percent while the Kings made just 35 of 87 shots (41.2 percent), including 3 of 20 from 3-point range.
This was the second time this season against the Jazz that Cousins has been ejected. The first time, the Kings won 108-97 on Nov. 24.
On Monday, the Kings were down 44-43 at the break but outscored Utah 19-11 to open the third, going up by seven on Thompson's 3-pointer with about 3 minutes left in the quarter.
Utah fought back, with Burks hitting a 3-pointer and DeMarre Carroll following with back-to-back scores.
Burks then blocked Thompson's shot in the lane to end the quarter, keeping the Jazz within 66-62.
The Kings led 82-75 lead with 4:26 remaining.
Utah went on an 8-0 run, Foye hitting a 3, Marvin Williams a pair of free throws then another 3 with 2:40 remaining to give Utah an 83-82 lead.
It was tied at 84 on a pair of free throws by Evans but he couldn't get his 3-foot runner to fall with 16 seconds left.
Jefferson ended up with the ball on the final possession after 3-point sharpshooter Foye was double-teamed.
Foye responded with a jumper to open overtime then four free throws to seal it.