Detroit's Brandon Knight missed a 3-pointer in the final seconds that would have tied the game after the Pistons trailed by 13 points with 3:26 left.
Jefferson helped the Jazz outscore Detroit 25-11 in the third, powering them to their first lead after trailing by as many as 15 points.
Utah also put together a 17-3 run after Austin Daye's 3-pointer with 8:38 left gave the Pistons the lead for the last time.
There was one comeback left, and it came up just short.
Detroit outscored the Jazz 12-1 and had a shot to send the game into overtime, but Knight was very short on a contested shot just before the buzzer. Knight and Pistons coaches lobbied for a foul, but didn't get what they wanted.
The Jazz (20-19) avoided falling under .500 and into a last-place tie with Minnesota in the Northwest Division.
Detroit had won seven of their last nine games.
Knight had 16 points and Greg Monroe scored 12 for the Pistons.