Parma acquired Giunti for the 1997–98 season, although he had a difficult season with the club, only making 13 appearances, as he was mainly kept on the bench. Halfway through his second season with Parma, after making only two appearances, he joined Milan in January 1999 (in a swap deal with Giuseppe Cardone), making six appearances, as Milan won the 1998–99 Serie A title that season. He played with Milan for two more seasons, during a dark period in the club's history, making 24 appearances in both seasons. He scored three goals during his Milan career; the first came in the UEFA Champions League against Galatasaray in 1999, the second against Fiorentina in the 2000–01 Coppa Italia and the third in a famous 6–0 win over city rivals Internazionale, in 2001.