The Mercury were without guard Diana Taurasi, who was a game-time scratch with back spasms.
Dupree scored seven points to key a 14-2 run that rallied the Mercury from a 52-45 deficit to a 59-54 lead with 1:41 left in the third quarter. Phoenix led the rest of the way.
Taylor made six straight free-throw attempts in the closing minute and matched a career high with a 13-for-13 performance from the line.
Hammon scored 11 first-half points, including a pair of 3-pointers, to help the Silver Stars open a 41-38 lead.