In his first season at Parma, Asprilla scored some important goals, including a 27-yard second-half free-kick which helped Parma defeat Milan 1–0, ending the Italian champions' unbeaten streak at 58 matches. It was at Parma Asprilla arguably enjoyed his greatest club success. Asprilla was part of the Parma squad which won its first international tournament, the 1992–93 European Cup Winners' Cup, scoring four goals in eight matches. It was his brace in Spain that rallied the Italian team to a 2–1 victory over Atlético Madrid in the semi-final. However, an injury meant he was an unused substitute as Parma defeated Belgian club Royal Antwerp 3–1 in the final.