Jason Maxiell added 14 points and seven rebounds for Detroit, which won its third preseason game in four tries.
The Jazz got 15 points apiece from Carlos Boozer and Ronnie Brewer.
Utah (1-2) never led in the second half but got as close as 84-81 when Jarron Collins hit a pair of free throws with 2:25 to play. Maxiell made a running jump shot and Carlos Delfino followed with a dunk to give the Pistons control.
Both coaches used their starters sparingly after the first quarter as the teams combined for 35 turnovers and each shot under 50 percent from the field.
The Pistons scored 12 points off Utah's 13 first-half turnovers and led 43-39 at the break. Murray, signed as a free agent to lighten the load on starters Chauncey Billups and Richard Hamilton, led the Pistons with 13 points on 6-of-10 shooting at the half.
Nazr Mohammed had 12 points for the Pistons (3-1) and Billups added 11 points and six assists.
Paul Millsap had 11 points for the Jazz. Andrei Kirilenko (back) and Derek Fisher (bruised pelvis) did not play.