Chicago took its first lead at 60-58 on a Deng 3-pointer with 4:26 remaining in the third and took the lead for good on a Boozer layup with 1:50 left.
Anthony Randolph and McGee each had 15 points for Denver, which lost four straight to end the preseason at 2-5.
Former Bulls guard Nate Robinson missed a potential game-tying 3-pointer with 18.1 seconds left.
Ty Lawson left the game with left groin tightness and scored 11 points in 16 minutes.
The Nuggets open Wednesday in Sacramento against the Kings.