Duncan also had a game-high 15 rebounds, while Rajon Rondo tallied a whopping 15 assists.
Rondo also led the Celtics with 22 points.
The Spurs took an eight-point lead into the locker room, which was just enough as the two teams went back and forth in the second half.
San Antonio shot 14-19 from the stripe for the game and were 8-16 from three.
And while Parker and Duncan were the two well-known names to fill the stat sheet for San Antonio, power forward Tiago Splitter was perhaps the game's most impressive player. He came off the bench to score 23 points on an efficient 9-11 shooting.
In fact, it was the bigs who may have been the difference in the game. The Spurs out-rebounded the Celtics by a healthy 41-25 margin.