Candice Dupree scored 16 points, Leilani Mitchell had 11 and Alex Harden added 10 off the bench for Phoenix (2-2).
Minnesota (3-1) was led by Maya Moore and Seimone Augustus with 17 points apiece. Lindsay Whalen added 13.
Phoenix used a six-point spurt at the end of the first quarter to take the lead and settled for a 48-38 edge at the half.
Both teams shot over 48 percent in the half, but the Mercury made 5 of 8 from beyond the arc and Minnesota was 0 of 4.
The Lynx went over three minutes early in the third without scoring, and Phoenix ran its lead to 17 after a pair of Monique Curry free throws.
Phoenix's Brittney Griner served the fourth of her seven-game suspension due to her offseason domestic violence incident.