Parker scored 16 in the second half Tuesday to get the Spurs in position to advance to the conference finals with a win Thursday in Oakland.
San Antonio outscored Golden State 55-40 in the final 24 minutes and scored 18 points off 11 turnovers by the Warriors.
Harrison Barnes led Golden State with 25 points and seven rebounds. The high-scoring tandem of Stephen Curry and Klay Thompson combined for a modest 13 points.
San Antonio shot 51.9 percent from the field to 47.3 percent for Golden State and outscored the Warriors 26-19 in the fourth quarter.