The Pacers led by as many as nine points early in the fourth quarter and still had a 95-91 cushion when George Hill hit a jumper with 5:29 to play.
Indiana managed only two more points the rest of the way while the Spurs were becoming the first team in the NBA this season with 10 victories. The Pacers had won their previous two games.
San Antonio took the lead for good on a jumper by Parker with 4:03 to play. He made 15-of-23 shots from the field and had support in the form of 22 points and 17 rebounds from Tim Duncan.
Manu Ginobili added 19 points for the Spurs, who have defeated Indiana in each of their last 11 meetings dating to April, 2007.
David West led Indiana with 22 points.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Biologists detail four new deep-sea 'killer sponges'