Stephan El Shaarawy, who was Milan's hero in their midweek 2-0 win over Cagliari, put Massimiliano Allegri's side in front early in the second half but Daniele Galloppa equalised in the 66th minute to earn Roberto Donadoni's side a point, which leaves them just a point behind their visitors.
Both sides had chances to win it in a game which came to life in the second half after a drab opening 45 minutes.
Parma took a very defensive approach to the game, allowing Milan to come at them early on.
But despite their possession, Milan were unable to create any chances of note until the 41st minute when Bojan Krkic's shot narrowly missed the angle of post and bar.
The game opened up in the second half, with El Shaarawy putting Milan in front in the 50th minute with a bold run into the penalty area which ended in him sliding his shot beyond the reach of Nicola Pavarini into the far corner.
Kevin-Prince Boateng missed the chance to make it two just minutes later when he found space inside the penalty area and was picked out by Krkic, but he headed just wide of Pavarini's goal.
Parma responded with a dangerous cross which Christian Abbiati pushed out to Musacci at the far post, but he was unable to find a telling touch as the goalkeeper recovered to defend his goal.
Pavarini pushed another Boateng effort wide of the post as the game swung from end to end.
In the 66th minute, Parma levelled with Galloppa's shot taking a slight deflection off a team-mate to nestle in the bottom corner of Abbiati's goal.
The outcome of the game was open as both sides had chances, the best of which fell to El Shaarawy, but Pavarini saved his shot from just outside the area to help secure his side a point.