Rodney Stuckey added 17 for Detroit (6-20), which won consecutive games for the second time this season and had five scorers in double figures.
New Orleans (4-20) lost its fifth straight. Trevor Ariza led the Hornets with 26.
Both teams spent most of the game without their starting point guards. New Orleans' Jarrett Jack missed the game with a knee injury, while Pistons rookie Brandon Knight sustained a broken nose early in the game when he was hit by Monroe's elbow.
The Hornets led 44-41 at the half, but Monroe helped the Pistons take a 65-61 lead into the fourth quarter.
By that point, Carl Landry had left the game with a left knee injury, and the Pistons took advantage. Four straight points from Stuckey gave Detroit a 75-65 lead with 7:50 to play.
Greivis Vasquez, though, scored the first seven points in a 9-0 New Orleans run that pulled the Hornets to within a point with 5:22 to play. That was as close as the Hornets got, however. Monroe scored the next basket on an offensive putback, and Stuckey's jumper put Detroit up 83-76 with 1:45 left.
NOTES: Knight joined a Detroit injury list that already included Will Bynum (foot strain), Ben Gordon (shoulder) and Charlie Villanueva (ankle). Bynum and Gordon both hope to return to practice on Monday, while Villanueva is expected to miss most of the season. ... Chris Kaman, who was sent home by the Hornets while they tried to trade him, is expected to rejoin the team in the next two days. ... Jason Smith left the game in the fourth quarter after being floored by two separate shots to the head in the second half.