She followed up the song with the hits Judy's Turn to Cry, and the feminist anthem You Don't Own Me.
Gore died of lung cancer at New York University Langone Medical Center in Manhattan, according to her partner of 33 years, Lois Sasson.
"She was a wonderful human being - caring, giving, a great feminist, great woman, great human being, great humanitarian," said Sasson, a jewellery designer.
Brooklyn-born and New Jersey-raised, Gore was discovered by Quincy Jones as a teenager and signed to Mercury Records.
She graduated from Sarah Lawrence College with a degree in English/American literature.
Gore's other hits include She's A Fool, Sunshine, Lollipops and Rainbows, That's the Way Boys Are and Maybe I Know.
She co-wrote with her brother, Michael, the Academy Award-nominated Out Here On My Own from the film Fame.
She also played Catwoman's sidekick in the cult TV comedy Batman.
In the 1990s, Gore co-wrote My Secret Love for Allison Anders' film Grace of My Heart, released in 1996.
A couple of years later, she appeared in Smokey Joe's Cafe on Broadway.
Gore had been working on a stage version of her life with playwright Mark Hampton when she died.
In 2005, she released Ever Since, her first album in 30 years, but was sure to revisit older hits in front of fans.
"If I've learned anything in this business," she told The New York Times that year, "how stupid would it be not to do It's My Party when people come to hear it?"
She officially came out to the public when she hosted several episodes of the PBS series, In The Life, which dealt with gay and lesbian issues.
During the 2012 presidential campaign, Gore turned You Don't Own Me into an online video public service announcement demanding reproductive rights which starred Lena Dunham and Tavi Gevinson, among others
In the last few years, she performed at Feinstein's at the Loews Regency in New York and, along with Ronnie Spector and LaLa Brooks, headlined the She's Got the Power concert outdoors at Lincoln Center in 2012.
In addition to Sasson, Gore is survived by her brother and mother, Ronny.
