After his stint writing for Jay Ward, Burns formed a partnership with Chris Hayward and they created the series The Munsters and were hired by producer Leonard Stern as story editors for the CBS series He & She, for which they won an Emmy award for comedy writing. The last project between Hayward and Burns would be as story editors for the sitcom, Get Smart.
In 1969, Burns began a partnership with James L. Brooks after being impressed with the television pilot for Brooks' show, Room 222. Burns joined the Room 222 writing staff and later produced the series.
After Room 222, television executive Grant Tinker hired Brooks and Burns to develop a television series for CBS starring Mary Tyler Moore. In 1970, The Mary Tyler Moore Show premiered and became a critically acclaimed series. The Mary Tyler Moore Show spawned spin off series such as Lou Grant and Rhoda. Burns also wrote and produced three television series; "F.M.", "Eisenhower and Lutz" and "Cutters."
Burns has also done screenwriting for movies. Most notably, A Little Romance which he was nominated for an Academy Award for Writing Adapted Screenplay. He also wrote the screenplays Butch and Sundance: The Early Days, Just the Way You Are and wrote and directed Just Between Friends.