Gunton was born in Santa Monica, California, the son of Rose Marie (née Banovetz) and Robert Patrick Gunton, Sr., a labor union executive. He attended Mater Dei High School in Santa Ana, California, the Paulist Seminary St Peter's College, in Baltimore, Maryland, and the University of California, Irvine. A lifelong devout Roman Catholic, Gunton had initially planned to become a priest. Gunton served in the United States Army (1969–71), earning a Bronze Star for valor and the Vietnam Service Medal.
Gunton played the role of Juan Peron in the original 1980 Broadway production of Evita, earning a nomination for Tony Award for Best Featured Actor in a Musical for his performance. He later starred in the title role of a 1989 Broadway revival of Sweeney Todd and received a second Tony nomination for his portrayal. Additional Broadway credits include Working, King of Hearts, The Music Women, How I Got That Story, and Big River.
Gunton portrayed President Richard Nixon in a recreation of the Watergate tapes incident for Nightline. He also played President Woodrow Wilson in the film Iron Jawed Angels (2004). Gunton is also known for his guest starring role as Capt. Benjamin Maxwell in the well-received 1991 Star Trek: The Next Generation episode "The Wounded". Gunton played Warden Samuel Norton, the head of Shawshank State Prison and the primary antagonist in The Shawshank Redemption (1994) opposite Tim Robbins. Gunton played Cecil Dobbs in the 2011 film The Lincoln Lawyer.
Gunton also guest starred in the first season of Desperate Housewives and the sixth season of 24, where he portrayed United States Secretary of Defense Ethan Kanin. He signed on as series regular afterward and reprised the role of Kanin but now as the Chief of Staff to the new President, Allison Taylor, in the show's seventh season as well as the two-hour television prequel film, 24: Redemption. He returned again for the eighth season but this time as the President's Secretary of State. Gunton portrays Leland Owlsley in the 2015 TV series Daredevil. Gunton made a guest appearance on Law & Order: Special Victims Unit in January 2017.
