The Nets fell behind by seven after one quarter, but dominated the rest of the way to defeat the Spurs for the first time in seven tries.
Parker left Wednesday's game against Washington with tightness in his lower back and Duncan was rested in Thursday's contest.
That left Cory Joseph as the Spurs' leading scorer with 18 points. Danny Green pitched in 17 points and Patty Mills had 16.
San Antonio made just 39 percent of its shots and turned the ball over 17 times.
UPI Sports Results for September 20, 2014
UPI Sports Results for September 19, 2014