Jeremy Lin's driving layup capped a 10-0 run that tied it 95-all with 34.6 seconds left, but rookie Kawhi Leonard hit a 20-footer from the left wing to give the Spurs the win.
Duncan's block of Lowry combined with a pretty bounce pass on a James Anderson layup sparked a 6-0 run to break a 70-70 third-quarter tie.
Duncan and Parker returned to the starting lineup after sitting out Saturday's preseason opener against the Rockets in Houston.
Parker scored 11 of his 15 points in the first quarter to lead the Spurs to a 14-4 lead before the Rockets made a run to close the quarter down by six.
Houston's second-unit led by Morris put the Rockets up 53-51 at the half.