Alexander got her big break as Pam Tucker on the NBC sitcom The Cosby Show. She later starred alongside Whoopi Goldberg in the 1990 civil rights epic The Long Walk Home. Perhaps her most memorable role was the acid-tongued attorney Maxine Shaw on the FOX sitcom Living Single, a role she played for five years. She is the co-creator and co-writer of Concrete Park, a science-fiction graphic novel with Tony Puryear.

In 1992, she appeared in the short-lived sitcom Going to Extremes, which centered on a group of American students at a medical school on a fictitious Caribbean island named Jantique. In 2002, she played probation officer Dee Mulhern in the Showtime series Street Time, which ran for two seasons. In international cinema, Alexander played the role of Hidimbi in Peter Brook's adaptation of The Mahabharata. She also played a young Flora in the TV miniseries Mama Flora's Family.

She was married to artist/screenwriter Tony Puryear. She actively campaigned for Hillary Clinton and toured college campuses with Chelsea Clinton, during the 2008 Democratic Party primary.

Her voice is featured on The Bible Experience. She appeared in Toni Braxton's music video for "You're Makin' Me High". In 2009, she appeared in Criminal Minds in the Season 4 episode, "The Big Wheel", as Detective Lynne Henderson, who requests the BAU's help in investigating a serial killer in Buffalo, New York. She also appeared in the 2009 film La Mission opposite Benjamin Bratt. In 2011, she appeared in season 7, episode 13 of House M.D. where she played the character Ms. Fields.

Alexander has starred in season 2 of the Amazon original drama, Bosch, as Constance Irving. In 2017 she played Detective Latoya in the critically acclaimed horror film Get Out.