Tim Duncan led San Antonio with 26 points on 11-of-15 shooting.
Andre Miller led Philadelphia with 28 points on 12-of-14 shooting. Andre Iguodala added 25 on 10-of-15 shooting as both teams shot more than 50 percent.
Miller scored 16 points in the third quarter. His free throw with less than a minute remaining gave Philadelphia its first lead, 79-78.
Roger Mason made two free throws and hit a 3-pointer to give the Spurs a 96-91 lead with 8:10 to go, and it was tied at 104 with 1:15 left when Miller hit a reverse layup. Manu Ginobili made a layup to put the Spurs ahead 106-104, and Iguodala tied it with a dunk with 51 seconds remaining.
Parker missed an 18-footer, but the Spurs got the ball back and set up the winning shot without using as timeout when Ginobili stole Miller's pass with 15 seconds left.
The Spurs opened with a 40-19 first-quarter lead by matching a franchise record with eight 3-pointers in the first quarter. The best 3-point shooting team in the NBA, the Spurs finished 15-of-26 from 3-point range. They were ahead by 16 at halftime.
But the 76ers cut it to 74-66 on Miller's 3-point basket 4:47 into the second half. Miller drove past Ginobili to make it 78-74 with less than 3 minutes left in the quarter. Parker had a layup try blocked by Theo Ratliff and the 76ers came back down the floor and got another layup by Miller. He hit a 21-footer the next trip down and would quickly add two free throws for the 79-78 lead.
Notes: The 40 first-quarter points scored by San Antonio topped the team's season high of 39 points during a 123-88 victory over Golden State on Dec. 6. ... Spurs backup G Jacque Vaughn spent his second straight game on the inactive list now that C Fabricio Oberto is back from the sore left foot that kept him out of seven games. ... The Spurs' 3-point barrage followed the 76ers' latest trend on defense. Philadelphia had allowed their opponents to make eight 3-pointers per game (39.7 percent overall) the past seven games coming into Saturday. ... The 76ers finished their season-high six-game road trip 1-5. ... The 76ers have lost (16 of their last 17) games in San Antonio, not winning here in five years. ... Iguodala has scored 75 points his last three games.