Robert Parish scored 33 points and combined with Charles Bradley for an eight-point streak in the fourth period for host Boston.
With Boston trailing, 100-97, Parish scored on a dunk with 6:58 left. Bradley stole the ball from George Gervin and went more than half the length of the court for a dunk that gave Boston the lead for good with 6:42 left.
After Parish scored following an offensive rebound, Bradley again stole the ball from Gervin and dunked to give Boston a 105-100 lead with 5:55 to go.
"Gervin was packing them in, and we wanted Charles to deter him," said Boston Coach Bill Fitch. "His offense came off his defense. He played a dynamite game."
It was the Celtics' fourth straight victory and eighth in a row over San Antonio. The Spurs, who lost their fourth in five games, haven't won in Boston since April 1, 1979.
Boston took its biggest lead, 38-26, early in the second quarter, but the Spurs cut it to 60-55 at halftime. Quinn Buckner scored 14 of his season-high 20 points in the first half for Boston. He made nine of his first 10 shots.
Gervin led the Spurs with 31 points.