Camille Little had 14 points and Tanisha Wright added 11 for Seattle (14-14), which won the season series against San Antonio to claim a possible tiebreaker if the teams close the season tied.
Jia Perkins scored 17 points, Shenise Johnson had 16, Davellyn Whyte added 14 and Danielle Adams 13 for San Antonio (10-18).
The Silver Stars outscored the Storm 7-2 in the final 23.8 seconds to nearly steal the victory.
Johnson made a 3-pointer, stole the inbounds pass from Thompson and fed Perkins for a 3 that pulled San Antonio within 72-71 with 1.7 seconds remaining.
Whyte stole the ensuing inbounds and flung the ball in an apparent shot, which Thompson grabbed amid a series of officials' whistles. After conferring, the referees ruled the game clock, which did not start, should have expired in the final chaotic possession and ruled the game over.
Little and Temeka Johnson scored all but four of Seattle's final nine points, including a driving layup by the 5-foot-3 Johnson against San Antonio's 6-4 Jayne Appel for a 69-64 lead with 39.5 seconds remaining.
The physical matchup drew the best performance of the season from Thompson.
Thompson had nine points in the final 5:21 of the first quarter and then opened the second quarter with a 3 to give Seattle its first lead at 18-16.
After exchanging pushes and forearms while battling for position, Thompson delivered a crushing elbow to Shenise Johnson's neck and jaw that felled the second-year guard. Johnson left the court after sitting on the bench clutching her jaw for a few minutes while the foul was reviewed.
The blow momentarily sparked San Antonio, who scored the next six points to take a 41-39 lead.
Seattle responded with more aggression, attacking the rim in retaking the lead at 48-43.