Sophia Young added 19 points and Shameka Christon had 13 for San Antonio (19-11).
Tina Thompson and Ann Wauters each had 12 points and Svetlana Abrosimova had 11 for Seattle (13-17).
Young scored 13 points in the third quarter, helping the Silver Stars take a double-digit lead.
Hammon's 3-pointer capped an 8-0 run by San Antonio to open the third, prompting a timeout by Seattle coach Brian Agler. Katie Smith hit a 3-pointer out of the timeout to cut the lead to 46-39, but the Silver Stars' lead grew to as many as 12 points in the quarter.
Hammon went 5 for 7 on 3-pointers after going a combined 5 for 21 from long distance in her previous four games.
Hammon hit her fifth 3-pointer for an 86-63 lead with 2 minutes left after San Antonio rebounded a pair of misses by Christon and Hammon.
San Antonio went 6 for 20 in the final quarter, but maintained its lead.
The Silver Stars had a steal on five of the Storm's first seven possessions, but they only resulted in layups by Hammon and Christon for a 4-2 lead.
Danielle Robinson's 15-foot jumper gave San Antonio a 15-11 lead, but Seattle closed the final four minutes of the first on a 14-5 run. Thompson and Tanisha Wright each made a 3-pointer during the run for a 25-20 lead after the first.
Hammon scored three straight baskets to cut Seattle's lead to 27-26 with 6 minutes left in the first half. Christon's 3-pointer a minute later gave the Silver Stars a 29-27 lead, their first since 15-13.
Christon and Hammon hit consecutive 3-pointers to give San Antonio a 37-31 lead, but Seattle responded with a short jumper by Wauters and a 3-pointer by Shekinna Stricklen.
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