The shortest running show for which an actor won a Tony was mentioned below by Wayman. I think it's worth noting that if the Tony seasons back then had aligned with the official season, Gray would not have won the award. Either Shirley Booth or Zizi Jeanmaire would have won.
Coming in a very close second was Zoe Caldwell's win for Tennessee William's Slapstick Tragedy, which ran seven performances.
