Detroit's Tracy McGrady scored 15 points to become the 59th player in NBA history to reach 18,000 points.
Indiana erased a 98-88 deficit with 4:45 to go and tied it 104-104 on Darren Collison's basket with 15 seconds left.
Prince missed a 13-footer at the regulation buzzer.
Ben Gordon scored the first four points of the extra session and finished with 16 points as the Pistons improved to 5-1 in overtime this season.
Prince's only miss in the first half came at the free throw line. He was 7 for 7 and scored 15 points as the Pistons shot 64.3 percent en route to a 60-55 llead.
Rodney Stuckey added 18 points and six assists for Detroit.