Inter had won six of its past seven league matches heading into the game at Parma, scoring 17 goals and conceding just one.
It was Parma which had the better of the earlier chances, but Inter broke the deadlock nine minutes into the second half.
Lukaku chested down a pass on the edge of the area and tried to turn but the ball ended up ricocheting into the path of Sánchez. Sassuolo defender Riccardo Gagliolo tried to clear his shot off the line but it had already gone over.
Lukaku did even better eight minutes later as he powered through from his own half and then rolled a great ball across for Sánchez to drive into the bottom right corner.
Parma briefly threatened a comeback when Hernani volleyed in Germán Pezzella’s cross in the 71st.
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