Buriani played 7 seasons (165 games, 10 goals in Serie A between 1977–1982) in the Serie A for A.C. Milan, A.C. Cesena, A.S. Roma and S.S.C. Napoli. A serious injury forced him to retire prematurely in 1985. He won the 1978–79 Serie A title with Milan. He made his debut with the club on the 11 September 1977, in a 1–1 away draw against Fiorentina in Serie A; he left the club following their second relegation to Serie B in 1982. In total he made 180 career appearances, scoring 14 goals, 13 of which came in Serie A, in 146 appearances.