Parker also dished off eight assists while Tim Duncan donated 17 points and 11 rebounds for the top-seeded Spurs, who took the early advantage in their best-of-seven Western Conference quarterfinal series.
The victory was the 11th straight for San Antonio, which fell in a first-round series to Memphis last year.
The eighth-seeded Jazz were led by Paul Millsap with 20 points and nine rebounds.
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