Camille Little scored 13 points and Shekinna Stricklen added 11 for the Storm (1-1).
Candice Dupree had 18 points and Brittney Griner added 17 points, seven rebounds and three blocked shots to lead the Mercury (0-2). DeWanna Bonner scored 11 points and Diana Taurasi had 10.
Seattle overcame an early 11-point deficit behind 8-for-19 shooting on 3s.
After Taurasi's jumper pulled the Mercury to 68-67 with 2:31 to go, Noelle Quinn followed with a basket 20 seconds later. Little's late shot from beyond the arc with 57.6 seconds remaining stretched the lead to 73-67.
Dupree's jumper pulled Phoenix within four with 7.2 seconds remaining, but Wright made two free throws 2 seconds later to seal the win.
Bonner's 3 with less than a second left provided the final margin.