The Pistons overcame a 14-point deficit in the first half to win for the fourth time in five games.
Stuckey scored 35 points while hitting 11-of-12 from the foul line. Monroe added 32 points and 11 rebounds and Prince had seven assists along with 28 points.
Detroit recorded only its fourth road win in 20 tries this season.
Tyreke Evans had 23 points for the Kings but he twisted an ankle in the fourth quarter and had to be helped off the court.