The Pistons had won two in a row, but were outscored by 22 points over the second and third periods. Utah led by as many as 29 in the fourth quarter.
Burke scored 20 points and handed out 12 assists. Enes Kanter added 18 points, Marvin Williams had 17 and Derrick Favors contributed 11 rebounds for the Jazz, who have alternated between a win and loss during their last seven games.
The two Detroit victories came after they had lost seven straight. Rodney Stuckey led the Pistons with 21 points.
It was the sixth road win of the season for Utah in 22 tries.