The Nerazzurri could have broken the deadlock after 17 minutes but Ezequiel Schelotto could only fire straight at Parma keeper Antonio Mirante from just six yards out.
With both sides struggling to create anything clear-cut, it was the Gialloblu who nearly opened the scoring after 70 minutes with Amauri involved again.
This time the former Juventus striker set up Nicola Sansone, but his powerful effort flew just wide of Inter's goal.
Ten minutes later it was the home side who grabbed the winner through veteran forward Rocchi in somewhat fortuitous fashion. The 35-year-old's shot bobbled off his standing leg to deceive Mirante and give Inter the victory.