The state's request to lift the stay went to Justice Ruth Bader Ginsburg, who oversees Connecticut cases. Ginsburg referred the request to the full court, which voted behind closed doors.
Ross, a graduate of Cornell University, has admitted killing at least eight women and girls, raping some of them, during the 1980s.
It is not immediately clear whether Ross will be executed early Friday morning as scheduled. The judge who issued the stay has also issued a restraining order that may delay the execution for more than a week while Ross's mental state is evaluated.
A group opposed to the execution contends Ross's years on death row have affected his mental competency.