Courtney Vandersloot grabbed the rebound off her own missed runner and passed out to Quigley, whose 3-pointer made it 94-82 with 52.3 seconds left. Vandersloot finished with 14 points and 12 assists for Chicago (4-9), which ended a six-game slide.
The ejection came during the middle of an 11-2 Chicago run that ended with a 69-60 lead late in the third. Phoenix cut the deficit to 71-67, but got no closer.
Griner managed 19 points and 10 boards before leaving the game and Diana Taurasi added 18.