Francesco Modesto struck the winner for Parma eight minutes from time after Napoli’s Giuseppe Mascara had equalised following Massimo Gobbi’s 57th-minute opener.
Milan’s Antonio Nocerino, scoring against his former club, Robinho and Antonio Cassano were all on target as disappointing Palermo were torn apart at the San Siro.
Napoli remain a point behind leaders Juventus, who visit Chievo Verona on Sunday, with 10 points. Parma are a further point back and 11th placed Milan are three points off top spot.
Earlier on Saturday, Inter Milan suffered their fourth loss in sixth Serie A matches, going down 2-1 at Catania.