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The Gialloblu had another chance soon after when Jonathan Biabiany latched onto a ball over the top before firing his strike over the bar.
Parma were in control and Biabiany threatened again when his low shot deflected wide of the far post.
After the break, the hosts continued to press and Cassano came close with a header that was saved by Anania.
Just past the hour mark, Parma made their dominance count as Amauri powered in a header from Cassano's corner to give them the lead.
With 10 minutes of the match left, Amauri scored his second goal when his header was saved by the keeper, but he slotted home the rebound to seal the three points and a place in Europe for his side.