Boozer, who finished with 19 points, put in a layup and made one of two free throws to give the Bulls a 84-83 edge with 1:47 to play.
Chicago's performance at the foul line was key down the stretch. Boozer made four more free throws to make it 88-85 with 27 seconds left. Joakim Noah, who finished with 12 points and 11 rebounds, then put in a couple of free throws before Luol Deng hit 3-of-4 at the line to seal the win.
The Bulls, who had lost three of four going into the game, also got 18 points and nine assists from Nate Robinson
Utah, which had won four of its past five contests, outscored the Bulls 19-11 in the third quarter knot it up at 69 heading into the decisive final period.