The Spurs settled the contest by out-scoring the Jazz, 58-36, in the second and third periods.
Tim Duncan had 20 points, nine rebounds and three blocked shots for San Antonio. James White had 12 points and five rebounds, while Manu Ginobili had 12 points, four rebounds and three assists for the Spurs, who have split their last four games.
Parker went 5-for-5 from the field in the second quarter as San Antonio built a 58-43 halftime advantage.
Deron Williams and Gordan Giricek scored 11 points each for the Jazz, who had won three of their previous four games. Paul Milsap had 10 points, five rebounds and two blocks; Mehmet Okur had 10 points and five assists; and Carlos Boozer had nine points, seven rebounds and two steals.
It was Utah's 15th straight loss at San Antonio.