Danielle Robinson scored 20 points, including six free throws in overtime, and had eight assists for San Antonio (6-6). Jia Perkins added 15 points on five 3s in the Stars' second straight win. Jayne Appel had 11 points and 15 rebounds.
Sue Bird scored a season-high 23 and had nine assists while Camille Little scored a season-high 20 for Seattle (5-9), which had won four of seven after a 1-5 start before dropping its second consecutive game.
Adams' 3 with 6.5 seconds left tied the game at 71-all.
"I just knocked it down with confidence," said Adams, who scored all 10 of her points in the second half and overtime. "I just shot it like I shoot any other shot."
Robinson found Adams open in the corner, although Becky Hammon also was in the area.
"We both were right there," Adams said. "I just reached out and grabbed it, stepped back and knocked it down."
Bird hit a 3 to put the Storm up 70-68 with 44.8 seconds left and Nicole Powell hit one of two free throws to make it 71-68 with 18.9 seconds to go.
San Antonio led 62-53 early in the fourth quarter before Bird scored eight and Shekinna Stricklen six to rally the Storm. The Stars led by 12 in the first half.
Adams also hit a 3 and scored on a drive in overtime.
"She really hadn't finished well for us in a game," Stars coach Dan Hughes said of Adams. "That's a player stepping up and she carried it over into overtime. That was a big shot. She's capable of making that, we just had a hard time getting her going to that point."
Storm guard Tanisha Wright, who had a season-high 24 points on Sunday, sat out with a bruised knee. She had started all 13 games, averaging 10.6 points. She is day to day.
"We've been through this many times with various people," Seattle coach Brian Agler said. "Tanisha at times, Sue, Lauren (Jackson). We've had people out so that's not an excuse for us. We're a team. It's not a one-person show, so we've got to find a way to get it done."
Robinson hit 10 of 11 free throws in the game. She entered the game shooting 94 percent (32 of 34).
"My mom always said, 'It's a free throw, nobody's guarding you so you should make it,'" Robinson said. "So credit to my mom for pushing me in that area."
Bird got her 2,000th career assist with a pass to Alysha Clark in overtime.
The Storm return to action when they host Washington at KeyArena on Sunday at 6pm.