The Italian giant club, where Zlatan Ibrahimovic is involved, has only taken one point from its two first matches for the season.
It ended in a draw at home against Torino in the premiere last weekend and on Saturday, the team was left point-less away against newcomer Parma.
Former Norrköping player Pontus Almqvist, 25 years old, was substituted in in the 74th minute and three minutes later, he set up Matteo Cancellieri for the decisive 2-1 goal.
Parma had made a shocking start with 1-0 through Dennis Mann already after two minutes.
Christian Pulisic equalized in the 66th minute before the winning goal came.
Pontus Almqvist joined Parma before the season and previously belonged to Russian Rostov, from where he was loaned out during the war.
Last season, he also played in Italy, then in Lecce.