New Jersey lost on the road for the 12th straight time and has won just three games away from home all season.
Prince scored 22 points and had seven rebounds while Monroe delivered a double-double with a career-high 20 points and 11 boards. The Pistons ended a four-game losing streak.
Anthony Morrow led the Nets with 22 points. New Jersey's last win on the road came against Memphis Dec. 21.
The Pistons shot 48 percent from the field and made just 9-of-18 free throw attempts.