Initially a theatre actor, Fuccello appeared in Broadway productions of Butterflies Are Free, The Unknown Soldier and His Wife, and Are You Now, or Have You Ever Been? in the 1970s. His first notable screen role was as Mark Elliot in the daytime soap opera, Love is a Many Splendored Thing, from 1972 until its cancellation in 1973. He later portrayed the role of Paul Kendall in the ABC-TV daytime soap opera One Life to Live from 1977-79. He then had a recurring guest role on the original Dallas TV series as Senator Dave Culver from 1979-91. The character was the former stepson of Donna Culver Krebbs who was played by Susan Howard.