Jasmin Kurtic gave Parma the lead one minute before halftime but Franck Kessie levelled 10 minutes into the second half with a ferocious effort from 25 metres.
Alessio Romagnoli heaed Milan in front four minutes later, Hakan Calhanoglu added a third and Zlatan Ibrahimovic nearly got in the act when he headed wide from a Kessie cross.
Milan stayed seventh with 53 points which will be enough to qualify for the Europa League provided Napoli, who are sixth and have booked their place by winning the Coppa Italia, finish in the top six.
