The Spurs defeated the Grizzlies for the 15th time in 18 meetings.
San Antonio scored the first seven points of the third period to take a 10-point lead and held a narrow advantage the rest of the way. The Spurs won their second straight after losing three in a row.
O.J. Mayo had his best game of the season for Memphis, scoring 28 points. The Grizzlies had a three-game winning streak snapped.
San Antonio moved within 2 1/2 games of first-place Dallas in the Southwest Division.