This year the international prize, which is based in Houston, New York and London, was awarded for the 37th time.
Stivicic was awarded the prize at a ceremony in New York's Playwright Horizons theatre on Monday evening. The prize consists of an award of US $25,000 and a print by Willem de Kooning, the theatre portal TheaterMania reported.
The panel of judges consisted of BAFTA and Emmy Award winner Rebecca Hall, London National Theatre Associate Director Bijan Sheibani, actor Carmen Herlihy, Scottish playwright Rona Munro, U.S. director Liesl Tommy, and Chay Yew, artistic director of Chicago's Victory Gardens Theatre.
Stivicic was one of 12 finalists chosen from among 140 nominees.
3 Winters premiered at London's National Theatre in 2014. Set in Zagreb, Croatia, between the years 1945-2011, the play creates a portrait of an eclectic family held together by generations of formidable women, says the portal.
After the premiere, the play won outstanding reviews and was published by Nick Hern Books.
Born in Zagreb, Stivicic graduated in dramaturgy from Zagreb's Drama Academy and in 2004 she earned a master's degree at the Department of Theatre and Performance of London's Goldsmiths College.
She has authored a number of plays.
She has lived and worked in London since 2003. For the 50th anniversary of the Royal Court Theatre in 2006, she was selected by the BBC and the Royal Court Theatre as one of 50 young playwrights set to leave a mark in the British theatre in the next 50 years.