Angel McCoughtry scored 16 on Friday and the Dream edged the Silver Stars, 60-57.
Lindsey Harding added 14 points and Yelena Leuchanka had nine for Atlanta, which trailed 45-42 entering the fourth quarter.
Sophia Young scored 21 to pace San Antonio.
The game, which was tight throughout, was tied at 53 with just over five minutes remaining. From there the Dream unleashed a 6-0 run, getting baskets from McCoughtry, Harding and Leuchanka, to go on top for good.