Baker's professional acting career began at the Guthrie Theatre in Minneapolis, where he starred in roles such as A Christmas Carol, Peer Gynt, Hamlet and The Sound of Music. In the 1980s, after winning Star Search in 1983, Baker took up the role of Colton Shore, on the soap opera General Hospital, which he held for three years. For a year, he played Craig Lawson on All My Children, and then for seven years played Connor Davis on The Bold and the Beautiful. He also starred in the Star Trek: Deep Space Nine episode "One Little Ship" as Kudak'Etan.