Temeka Johnson, Noelle Quinn and Tanisha Wright added 12 points each to help the Storm (4-3) win their third straight.
Jia Perkins scored 21 points, Danielle Robinson had 20 and Shameka Christon added 19 for San Antonio (2-5), which lost its fourth straight despite a late rally.
The Silver Stars stole the ball with Seattle leading 88-84 with 21.5 seconds to play, but Christon lost the ball out of bounds after being tripped on a fast-break attempt. No foul was called on the play as the Storm regained possession and closed out the victory at the free-throw line.
Seattle was 23-for-25 on free throws and 6-for-9 on 3-pointers.
San Antonio struggled to find some familiarity early in the game with two new starters in the lineup.
Danielle Adams started in place of Jayne Appel, who missed her second straight game with a concussion, and San Antonio coach Dan Hughes opted to start Shenise Johnson instead of Christon.
The altered lineup led to some disarray, with the Silver Stars committing four turnovers in the first quarter.
Robinson fired an inlet pass to Adams, who had sealed off her defender, but the ball went sailing out of bounds because Adams was expecting Robinson to shoot. Both players were baffled, and that's how San Antonio played for much of the first half.
The Storm led by 12 points in the first quarter as the Silver Stars shot 4-for-14 from the field.
Seattle went on an 8-0 run, capped by a free throw by Johnson following a technical foul on Hughes.
Christon's return to the lineup stabilized the team's offense, yielding a 9-4 run.
Seattle coach Brian Agler left for the locker room before the halftime buzzer, upset with the Storm's execution on the final two plays of the first half. Wright passed up an open 3 in the corner as Seattle failed to put up a shot before time expired.
Agler's mood didn't improve when Christon's fourth 3-pointer gave San Antonio its first lead at 42-40 on the opening possession of the third quarter.
Both teams were without its All-Stars. San Antonio's Becky Hammon sat out with a broken right middle finger and Sophia Young is out for the season with a knee injury, as is Seattle's Sue Bird.
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