Parker missed Friday's 120-108 loss to the Los Angeles Clippers due to a contusion on his right quadriceps but he showed few ill effects from the injury Monday.
The four-time all-star guard dished off seven assists as San Antonio notched its 12th straight win over the Wizards.
Tim Duncan passed Clyde Drexler to claim 25th place on the NBA's all-time scoring list, scoring 14 points to bring his career total to 22,207, while also hauling down nine rebounds.
Tiago Splitter added 17 points and seven rebounds off the bench for the Spurs.
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