San Antonio shot 57 percent from the field, made all 10 of its free-throw attempts and converted 10 3-pointers -- including three each from Kawhi Leonard and Danny Green.
The Spurs broke the game open with an 18-point run late in the first half to take a 25-point lead at intermission and coasted from there.
Parker scored 18 points to lead the top-seeded Spurs, Leonard had 17 and Green added 13. Tim Duncan produced 12 points and 13 rebounds while playing only 27 minutes. San Antonio's bench registered 43 points.
Josh Howard and Al Jefferson were the only Utah players to reach double digits in scoring with 10 each.
The opening-round series will not resume until Saturday, when Utah will host Game 3.