Game 2 of the best-of-five series is set for Wednesday, also in Phoenix.
The Sky parlayed a dominating final four minutes of the second quarter into an 11-point lead at halftime. They extended the advantage to 13 points after three periods and to 23 points midway through the final quarter.
Phoenix fashioned an 11-0 run late in the game but it was too little, too late.
Allie Quigley added 18 points for the Sky, with Stefanie Dolson scoring 14 points off the bench, Candace Parker hitting for 16, Courtney Vandersloot contributing 12 points and 11 assists, and Azura Stevens adding 10 points for Chicago.
Brittney Griner led Phoenix with 20 points, while Diana Taurasi scored 17 and Skylar Diggins-Smith added 15 for the Mercury.
The Mercury led 25-20 after the first quarter behind 50 percent shooting from the floor and a 4-for-6 showing from beyond the arc.
Phoenix led 29-20 after a running layup by Shey Peddy a minute into the quarter, but then scored just six more points until halftime, missing 12 of its final 14 shots in the period and committing 11 turnovers in the first half, its most