Five minutes later it was the turn of Parma to come close to scoring, as Gianluca Musacci's free kick deflected narrowly over the Milan crossbar.
Sotiris Ninis created another good opportunity for the hosts to make the breakthrough in the 34th minute, when he excellently set up Dorlan Pabon, but Christian Abbiati parried away the Colombian's shot.
Five minutes into the second half, Milan broke the deadlock. Stephan El Shaarawy, who scored twice against Cagliari in midweek, was again on target for the Rossoneri, as he latched on to Massimo Ambrosini's pass before driving the ball home between the legs of Mirante.
It could have been 2-0 to Milan just moments later had Boateng been able to keep his header off a Bojan Krkic header on goal from just yards out.
That miss eventually came back to haunt Milan, as Parma levelled the score in the 66th minute.
Gianluca Musacci laid a free kick to Daniele Galloppa on the edge of the penalty box, and the Italian midfielder shot home with his left foot.