The Spurs open the regular season Oct. 31 at New Orleans.
The Wizards visit Cleveland on Tuesday in their regular-season opener.
Washington sat its starters for much of the fourth quarter after leading most of the game.
Jackson hit a 3-pointer to cap a 9-0 run at the close of the third quarter as the Spurs took a 74-66 lead after a slow start.
Washington held a 40-27 lead with 9 minutes left in the first half following an 18-8 run. The Wizards built their lead as the Spurs' starters sat for about eight minutes bridging the first and second quarters.
San Antonio rallied once its starting lineup returned, with Parker scoring eight points in an 18-5 run.
Boris Diaw scored on a fast-break layup to give San Antonio a 61-59 lead, its first since holding a 4-2 advantage. Parker set up Diaw's basket with a diving save out of bounds on a Washington miss.
The Spurs were without Manu Ginobili, who sat out with back spasms.
The San Antonio Spurs were in rare form in their demolition of the Oklahoma City Thunder on Saturday, but they refuse to rest on their Game 1 showing.
A disappointing 32-point loss for Oklahoma City in Game 1 of its series with San Antonio leaves the Thunder searching for answers.
When asked how he felt after Game 1 against the Spurs, Kevin Durant simply responds "I'm not telling you." When prodded a little more, he adds that they just need to move on to the next matchup instead of focusing on this one.