O'Connor was born on December 20, 1909, in Manhattan, New York City, the son of Irish immigrants.
O'Connor gained fame as a lawyer in 1953, when he defended Christopher Emmanuel Balestrero, a bass player at the Stork Club falsely accused of armed robbery.
The story was the basis of the 1956 Alfred Hitchcock movie, The Wrong Man, in which O'Connor was portrayed by Anthony Quayle.
In 1966, he was the Democratic Party nominee for Governor of New York, losing to Nelson Rockefeller.
He died on December 2, 1992, in Booth Memorial Hospital in Flushing, Queens, from head injuries he had suffered 13 days earlier when he fell down a flight of stairs at his home.