The foul shots were the last points of a season-best 36 points for Stuckey, who helped bring the Pistons just their 10th win in 32 games this season. Six of those victories have come in Detroit's last eight contests.
The Pistons overcame an 11-point deficit early in the third quarter and took the lead for good at 105-104 with 2:20 remaining on a 3-pointer by Brandon Knight.
After Stuckey's free throws put Detroit in front 112-108, Marcus Thornton missed a 3-pointer for the Kings to end their hopes.
Knight scored 23 points and had a career-high 10 assists. Tayshaun Prince added 22 for the Pistons.
DeMarcus Cousins produced his 19th double-double of the season for Sacramento, scoring 26 points to go with 15 rebounds. The Kings have dropped four in a row.