Stuckey's layup gave the Pistons a three-point lead and the teams combined to go 1-for-7 from the field with two missed free throws and two turnovers the rest of the way.
The lone basket down the stretch came from Al Horford, who brought the Hawks within one by hitting a layup with 5.6 seconds left to account for the final score.
Detroit then turned the ball over, but a jump shot just before the buzzer by Lou Williams was blocked by the Pistons' Andre Drummond to preserve the win.
The Pistons have won four in a row after opening the season with an 8-22 record.
Josh Smith scored 20 points for the Hawks, while Horford had 18 points and 15 rebounds.
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