Parker pumped in 24 points with 10 assists. Duncan helped out with 19 points and 11 rebounds.
Manu Ginobili made his season debut after missing time with back spasms, scoring eight points over 15 1/2 minutes, and Danny Green added 21 points as the Spurs remained unbeaten three games into the season.
The Jazz lost their second straight despite 29 points and nine assists from Mo Williams.
Paul Millsap provided a double-double of 17 points and 10 rebounds for Utah.