His death, in Sibley Memorial Hospital, resulted from complications of a fall, according to his nephew Christopher Buckley, the author and political satirist.
With his improbable victory, Mr. Buckley became the first third-party candidate to land a seat in the United States Senate since Robert M. LaFollette Jr. of Wisconsin was elected on the Progressive ticket in 1940.
He served only one term, from 1971 to 1977, and — although there was an effort to draft him for the Republican presidential nomination in 1976 — never won another election.
But President Ronald Reagan brought him back into public life, appointing him to a State Department post in 1981 and naming him president of Radio Free Europe/Radio Liberty in 1982.
In 1985, President Reagan named him to the United States Court of Appeals for the District of Columbia Circuit. Mr. Buckley served as a federal judge for 15 years, the last four as a semiretired senior judge.
The scion of an oil tycoon who left $17 million to each of his 10 children, Mr. Buckley had none of the polysyllabic pyrotechnics of his younger brother William F. Buckley Jr., the conservative author and commentator who founded National Review and hosted the PBS program “Firing Line.”
But he was a patient, tenacious voice in a tumultuous era of racial violence, campus unrest and protests against the war in Vietnam.