Boys and Girls earned a special jury prize for its four-person ensemble cast.
Fairchild received the honor at a Miss Subways reunion luncheon at Ellen's Stardust Diner.
Tom Stoppard's drama also stars Romola Garai.
The play returns to New York for the first time in 42 years.
Harvey Fierstein hosted the ceremony, which toasted longtime theater industry professionals.
The critically acclaimed production is now running at the New Victory Theater.
The Pulitzer Prize-winning comedy stars James Earl Jones and Rose Byrne.