Stuckey, who came back after a three-game absence due to a toe injury, scored 12 of his 24 points in the fourth quarter and the Pistons overcame a 12-point deficit in the period to snap a five-game losing streak.
Trailing, 67-55, in the early stages of the fourth quarter, Stuckey and the Pistons stormed back with a 19-6 run.
Stuckey capped the surge with a triple, giving Detroit a 74-73 advantage with 55.9 seconds left.
Nene gave the Wizards the lead right back with a hook shot off the glass, but Greg Monroe's tip-in at the other end made it 76-75 in favor of Detroit with 23.1 remaining.
A bit later, after Ben Wallace made 1-of-2 from the stripe, Nene tied the game at 77 with a sweeping hook in the paint with 5.8 ticks to go.
But Stuckey quickly dribbled up the floor and drained his pull-up jumper from the right-elbow for the win.
Prince netted eight first-quarter points as the Pistons took a 16-14 edge into the second.
Despite shooting just 27.8 percent and turning the ball over 13 times, Detroit found itself down just 35-30 heading into the break. The Pistons out-rebounded Washington, 29-21, and were 9-of-11 from the foul line in the half.
The Wizards led 62-53 after three quarters.