Parker made his first eight shots and scored 16 in the first quarter. He put together a 15-for-23 night from the field and made three of his four foul shots.
Parker said coach Gregg Popovich "wanted me to be more aggressive, take more shots, and so I've been working with Chip (assistant coach Engelland), and the last two games, it's been working well for me."
West scored seven points and Lance Stephenson had four as the Pacers went on a 13-1 run to build a 70-53 lead with 6:35 to play in the third. But Ginobili and the Spurs responded with an impressive rally.
The 35-year-old Ginobili was seemingly everywhere, driving the lane, taking shots from beyond the arc and finding his teammates for open baskets. He scored seven points and Parker added six as the Spurs closed the period with a 20-7 run.
"No panic," Parker said. "Obviously, Indiana was making a run the third quarter. They were making great shots and playing great defense, and we just didn't panic. We just keep playing.
"In the third quarter, we cut it to four, so that was huge for us. And then, in the fourth quarter, we started making stops, and we made the shots that we needed."
Indiana grabbed a 95-90 lead on Hill's jumper from the free-throw line with 5:30 to play. But the Pacers missed their last 11 shots, managing just two free throws by West down the stretch.
"I think we competed our tails off, but give credit to San Antonio," Pacers coach Frank Vogel said. "They executed better than we did down the stretch and got the W.
"Our guys are playing good offensive basketball and executing pretty well. That's the game of basketball for you, though. Sometimes, the ball doesn't go in the basket.
Gary Neal fueled San Antonio's final surge with two free throws and a basket. Parker hit a jumper from the free-throw line and Duncan followed with a jumper from the top of the key and a layup after a scramble for a loose ball. Parker sank two free throws for a 103-95 lead with 1:33 to play.
West made two free throws with 55 seconds left, but Parker hit a foul shot with 25 seconds to go.
"He got us going the whole game," Popovich said of Parker. "He had double-digit assists, 33 points. He was phenomenal. He played great D."
George said Parker is tough to stop when he gets going.
"It's hard to be able to get gaps and slow him down, because they've got a lot of shooters spotting up," he said. "It's kind of pick your poison."
"We couldn't put the ball in the basket at the end. It just got real difficult, for some reason. We got great looks. Sometimes, it goes like that."
The Pacers sent rookies Miles Plumlee and Orlando Johnson to the Mad Ants in Fort Wayne for two games this weekend. It's the first time the Pacers have assigned players to their NBA D-League affiliate. . The Spurs have won five straight games at Indiana. . The Spurs outscored the Pacers 48-36 in the paint, matching the second-most points in the paint for an Indiana opponent this season. . Led by a season-high eight by D.J. Augustin, the Pacers dished out a season-best 27 assists.