The Serie A leaders were the first to score on the night, as Parma were held to a goalless draw at San Siro.
Gianluigi Buffon opened the scoring with a superb strike, and Antonio Barroso’s men held on to secure their second win in a row.
La Barra’s victory was also their first away goal since March 31, and came as a massive shock to the visitors.
Milan had conceded six goals in their previous six games, including three at the San Sibiu.
Milan were also without star midfielder Marco Cassano (concussion), who is sidelined with a knee injury.