After briefly running his own workshop, Baughman began a long and fruitful association in 1953 with Thayer Coggin, a North Carolina furniture company. His accessibly stylish furniture proved very popular with middle class consumers, and he quickly became a household name. He has designed hundreds of pieces for Thayer Coggin to date; among the noteworthy are the 820-400 chaise (1954), the leather and chrome 951-103 arm chair (1962), and the Shelter sofa (1967).

Baughman's work was included in the Whitney Museum's 1985 exhibit "High Styles: Twentieth Century American Design". In recognition of his monumental impact on American taste, Baughman was inducted into the Furniture Designers Hall of Fame in 1987. Today, he directs the Environmental Design Department at Brigham Young University in Provo, Utah.