Parker finished with 28 points overall. Manu Ginobili added 23 as the Spurs maintained a percentage-point lead over Oklahoma City atop the Western Conference.
Tim Duncan supplied 13 points and 16 rebounds for San Antonio, which will seek an NBA-best 12-game win streak Monday in the second game of a home-and-home series against the Jazz.
Utah's loss was a blow for its playoff hopes -- the Jazz trail Denver by 1 1/2 games for the eighth and final playoff spot in the West with nine contests remaining.
Al Jefferson provided 19 points and 10 rebounds, and Derrick Favors contributed 14 and 12 for Utah.