He played the unbalanced informer Herbert Gelman on Broadway in the original production of Advise and Consent (1961), for which he won the Fanny Kemble Award.

In 1967 he appeared as Brock in the fourth season of the science fiction TV show Voyage to the Bottom of the Sea in the episode "Fatal Cargo".

He later appeared as storekeeper Ike Godsey in The Homecoming: A Christmas Story (1971), the TV movie pilot for The Waltons (1971); The Moneychangers (1976); Backstairs at the White House (1979); and, in his only regular role, the short-lived 1979 CBS series Time Express.

Parfrey's frequent association with that film's director, Franklin Schaffner, also included his role as Maximus, one of the three "See No Evil" orangutan judges in Planet of the Apes (1968).

His many film credits also include parts in Cattle King (1963), The War Lord (1965), The King's Pirate (1967), How to Save a Marriage and Ruin Your Life (1968), Madigan (1968), Sam Whiskey (1969), Cold Turkey (1971), Dirty Harry (1971), Oklahoma Crude (1973), Stay Hungry (1976), The Incredible Journey of Doctor Meg Laurel (1979), Carny (1980), Bronco Billy (1980), Used Cars (1980), The Seduction (1982), Frances (1982) and Jinxed (1982).