Burini played for 12 seasons (330 games, 123 goals) in the Italian
Serie A for
A.C. Milan and
S.S. Lazio. He made his debut with Milan at the age of 20, in an 8–1 win over
Bari, marking the occasion with a brace. He scored 12 goals during the
1950–51 Serie A season, helping Milan capture the league title after a 44-year wait, and also won the
Latin Cup later that season. He is remembered by Lazio fans for his contribution to winning the first major trophy for the club, the
Coppa Italia in 1958, and for his performance in two
Derby della Capitale games against cross-city rivals
Roma: in Lazio's 1955 3–1 Rome Derby victory, he scored two goals, and in the 1958 edition of the Rome Derby, he scored one and set up
Arne Selmosson for another in a 2–1 victory. ==International career==