On a drive to the basket, Stewart cut off Taurasi, who then threw a behind-the-back pass to Brittney Griner for a layup. Phoenix trailed 64-49 after the bucket.
The 38-year-old Taurasi underwent back surgery before the 2019 season, and hamstring problems limited her to six games last year.
Phoenix put up a fight and drew within 70-66 on a pair of Sophie Cunningham free throws with 26 seconds left before the Storm sealed it at the free throw line.
After Alanna Smith’s layup gave Phoenix a 16-14 lead with 95 seconds left in the first quarter, Seattle’s Breanna Smith made a layup and Sami Whitcomb a 3-pointer near the end of the quarter. Loyd started the second with back-to-back 3s, Whitcomb made another layup and Seattle began to create separation.
Griner led Phoenix with 20 points.