The Spurs began a six-game journey that will also take them to Indiana, Toronto, Washington, Orlando and Miami. They improved their road record this year to 5-1.
Duncan scored 20 points and grabbed 15 rebounds, hitting 7-of-12 shots from the field while the Spurs were hitting 58 percent as a whole.
Tony Parker was 12-of-17 and finished with 26 points. Tiago Splitter came off the bench to hit 9-of-11 and score 23 points.
San Antonio took an eight-point lead into the fourth quarter, outrebounded Boston by 16 and allowed the Celtics only one offensive rebound.
Rajon Rondo had 22 points for the Celtics and Paul Pierce scored 19. Boston lost its second straight and fell to 3-3 at home.