When Cicely Tyson was asked to star in “The Trip to Bountiful” on Broadway this spring, she knew some people might regard it as a marketing ploy. Her role was originally conceived as a white character, after all, with Geraldine Page winning an Academy Award in the 1985 film version.

But at Sunday’s Tony Awards, Ms. Tyson made history with her performance. Not only did she become the oldest person to win a Tony, at the age of 88, but she and another black actress — Patina Miller in the musical “Pippin” — earned Tonys for roles that were not created for black women. Such performances, like Audra McDonald’s in the 1994 Broadway revival of “Carousel,” are very rare.