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.