Harden was whistled for his fifth foul on the ensuing jump ball, forcing Houston coach Kevin McHale to sit his leading scorer.
"It changed the entire game," Harden said of the call. "It gave me five fouls. I had to come out, and then I had to play hesitant. It changed the entire game."
The Spurs stretched their lead to 19 points in the fourth quarter before the Rockets rallied, but were unable to get closer than the final score.
"I think it was the start of the game," McHale said. "We had to fight back. I was proud of the guys and how they battled back."
San Antonio set season highs with 41 points in the first quarter and 69 in the first half but Houston kept pace with 63 before halftime — the most by a Spurs opponent this season.
The Spurs shot 67 percent in building a 21-8 lead in the opening 6 minutes.
Cole Aldrich's running hook gave the Rockets their first lead at 65-64 with 1:05 remaining in the half. Ginobili made a 3 and a layup to stake the Spurs to a 69-65 lead at halftime.
Danny Green was 5 for 7 on 3-pointers and finished with 17 points for San Antonio.
NOTES: Rockets P Patrick Patterson (bruised right foot) missed his seventh straight game. ... Parker is the only player in the NBA averaging at least 18 points, 7 assists, and 3 rebounds while shooting over 50 percent from the field, 40 percent on 3s, and 80 percent on free throws. ... San Antonio has five winning streaks of at least 3 games this season. ... While the Spurs rank first in total assists at 25.8 per game, Parker is the only player who has more than 10 in a game. He has done it six times.