The Spurs bounced back from a home loss to Houston 24 hours earlier by fighting off a Dallas comeback.
The Mavericks scored 12 points in a row in the fourth period to close within one, but Tim Duncan then scored six consecutive points for the Spurs and Danny Green made his fifth 3-pointer of the contest to fight off the rally.
Dallas climbed back within three in the final minute, after which Ginobili and Parker made two free throws each in the final 34 seconds to clinch the victory.
Parker, who had only six points in the loss to Houston on Christmas Day, scored 23 against the Mavericks. Green went 5-of-5 from 3-point range and scored 22 points while Duncan had 21 points and 13 rebounds.
Dirk Nowitzki had 25 points to pace the Mavericks.