Jefferson scored 16 points and yanked down 10 rebounds for the Jazz, who broke a four-game losing streak.
Marvin Williams and Enes Kanter led a strong performance from Utah's bench with 14 points apiece.
The Pistons, meanwhile, tumbled to their sixth straight defeat and lost guard Brandon Knight, who left the game with what appeared to be a sprained ankle in the first quarter.
Greg Monroe accounted for 15 points and 13 rebounds for Detroit.
Rodney Stuckey and Jonas Jerebko each netted 15 points.