Jones was born in New York City, New York, to a musician father. Her mother is Jewish and her father is African-American. Jones performed in the children's chorus of the Metropolitan Opera as a youth and graduated from the Berkeley Carroll School in 1999. "I did theatre all throughout middle school and high school and was really into it, the same with singing," she said. Jones received her BFA in drama from the North Carolina School of the Arts, and appeared in the national tours of Rent and Caroline, or Change.
In 2007 Jones made her Off-Broadway debut in Passing Strange, which transferred to Broadway on February 28, 2008. She created the role of Whatsername in the Green Day rock opera American Idiot, which opened on Broadway on April 20, 2010. Paper magazine said of Jones, "She's carved out a nice niche for herself as the girl to call when there's a cooler-than-thou musical in town."
In 2012 Jones played the Narrator in Manhattan Theatre Club's Off-Broadway musical Murder Ballad, for which she received a Lucille Lortel Award nomination for Outstanding Featured Actress. Jones returned for the show's engagement at the Union Square Theatre, which ran from May 22, 2013, to July 21, 2013. Later that summer, Jones appeared in a new musical adaptation of Love's Labour's Lost at Central Park's Delacorte Theater.
On June 2, 2014, Jones received a Lilly Award, a prize designed to honor women in the theater.
On April 14, 2015, Jones replaced Lena Hall as Yitzhak in the Broadway production of Hedwig and the Angry Inch. Jones played the role through the production's end on September 13.
