After forcing a turnover on a jump ball won by Elena Delle Donne with 17.4 seconds left, Cappie Pondexter worked into the lane, found Courtney Vandersloot on the left wing and Vandersloot dribbled back across the free throw line before passing to Quigley on the right wing for the winning shot. Kara Lawson missed an off-balance 3-pointer from the right corner as time expired.
Quigley finished with 20 points. Delle Donne led the Sky (16-11) with 22 points, and Vandersloot had 10 assists.
Emma Meesseman topped the Mystics (15-10) with 20 points, including a jumper after an offensive rebound with 29 seconds left for an 85-82 lead. Pondexter, who had 11 points, countered with two free throws at 20 seconds.
Tamara Young set a Chicago record, playing in her 186th game.