The attractive Goodman harbored dreams of a show business career from age six when she saw the film version of "The Sound of Music". She spent her formative years in Manhattan and dreamed of attending the famed High School of Performing Arts, but to her dismay was not accepted. Devastated at the rejection, Goodman abandoned her aspirations, obtained a degree at the Fashion Institute of Technology and found work. Bored by a dead-end job, she quit working and enrolled as a drama major at the City College of New York, eventually graduating cum laude. Recognizing the difficulties of being both female and a woman of color, Goodman began developing her own one-person show "Things Going On", which she spent close to seven years developing. Then HBO chief Michael Fuchs was intrigued by an invitation to one of her performances and attended, an event which led to Goodman headlining her own one-woman special "Hazelle!" on that network in 1995. An outgrowth of her stage show, Goodman portrayed a variety of characters, ranging from an elderly Southern woman whose son has been stricken with AIDS to a well-endowed gospel singer. Critical reaction was positive with many reviews comparing Goodman favorably with Whoopi Goldberg.
By that time, Goodman had begun to make inroads in features, playing the bit role of a neighbor in "True Identity" (1991) and appearing as the mother of a prostitute in one scene of Michael Mann's "Heat" (1995). More recently, Goodman had the recurring role of crime queen Georgia Rae Mahoney, out to revenge her brother's death, in the NBC drama series "Homicide: Life on the Street"