The Pistons ended a brief two-game Milwaukee winning streak, hitting eight 3-pointers while the Bucks could manage only one.
Detroit turned an eight-point halftime deficit into a 14-point lead by outscoring the Bucks in the third quarter 33-11.
Monroe hit six field goals in the third period while Brandon Knight was producing 10 points.
Knight finished with 20 along with five assists. Jason Maxiell added 10 points in what was Detroit's fifth win in six games.
Milwaukee was led by 15 points from Brandon Jennings, but he converted just 5-of-13 attempts.
The Pistons won on the road for the fourth time in 18 games this season.
2014: The Year in Music [PHOTOS]