Milan looked to have taken the lead in the 10th minute after Lucas Paqueta found the back of the net but it was ruled out for offside after a VAR review.
The hosts were frustrated for the rest of the half but had the ball in the net again four minutes into the second half through Piatek, and this time it stood.
It was a seventh goal in only six games for the club for the former Genoa man and was swiftly followed by a second from Franck Kessie.
Samu Castillejo set up Kessie for a right-footed shot from the right side of the box, and it was Castillejo who netted the third in the 67th minute from an Andrea Conti cross.
The hosts then fell foul of the VAR system for the second time when Fabio Borini's strike was also ruled out for offside.