Tanisha Wright also scored 19 points and Shekinna Stricklen added 13 to help the Storm (9-11) win for the third time in three meetings with the Mercury this season.
Candice Dupree led Phoenix (10-11) with 18 points and eight rebounds. The Mercury have lost four of their last five overall.
Seattle shot only 29 percent from the field in the first half but still led 31-30 at the break. The Storm then took control in the third while Phoenix lost starters Brittney Griner and DeWanna Bonner.
Griner landed awkwardly on her left foot, hurting her ankle, with 1:47 left in the period. The team said X-rays on her left foot were negative. Bonner, the Mercury's second leading scorer, sprained her right knee with 4:44 left in the third. Neither player returned to the game.
Seattle scored nine straight points and outscored Phoenix 30-17 in the period to take a 61-47 lead.
Seattle, the worst rebounding team in the league, outworked Phoenix 38-30.
Griner had nine points and four blocked shots when she left while Bonner had 11 points and four rebounds for the Mercury.
Diana Taurasi, the league's leading scorer, was held to nine points on 2-of-11 shooting for Phoenix. She also had five assists.
Thompson scored five of the Storm's nine straight points in a third quarter stretch as Seattle broke a 38-all tie.
Despite missing nine of their first 10 shots in the second quarter, Seattle held a 31-30 lead at the break. The Storm were only 10-of-35 from the field in the first half but made six straight free throws in the final 1:23 to get the lead.
The Storm beat Phoenix 75-72 on June 2 and 88-79 on Aug. 1, both in Seattle. The Storm have won eight of the last nine meetings between the teams, dating back to 2011.
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