Monique Currie had 12 points and Cayla Francis 11 for the Mercury (3-3), who pulled away with a 16-5 run in the middle of the second quarter to a 38-28 lead.
Sue Bird rallied the Storm (2-4) within 71-69 when she put back her own missed 3-point attempt with 5:18 left in the game. But Phoenix closed on a 13-3 burst as Seattle's offense suffered a pair of shot-clock violations in the final 1:30.
Crystal Langhorne had 13 points to lead the Storm. Bird and Alysha Clark added 11 each.
Phoenix was 7 of 17 from 3-point range while Seattle was just 1 of 13.
It was the sixth contest of Brittney Griner's seven-game suspension for a domestic violence incident.