The 12-game winning streak is the first by San Antonio since Nov. 1-24, 2010.
The Spurs also pushed their winning streak over the Kings to nine games overall and 11 straight in Sacramento. They have won 30 of the last 33 in the series.
Tim Duncan added 10 points with nine rebounds and six assists for the Spurs.
Isaiah Thomas paced the Kings with 18 points despite shooting 7-of-17 from the field. DeMarcus Cousins registered 15 points with 13 boards and Rudy Gay chipped in 14 points in the setback, Sacramento's sixth in its last eight games.