Chievo then took the lead in the 36th minute when Zukanovic met Valter Birsa's free kick and guided the ball into the bottom corner from inside the six-yard box.
Alberto Paloschi came close to scoring a second for his side at the beginning of the second half, but, after dribbling into the box, he saw his low effort deflect narrowly wide of the post.
Paloschi threatened again just past the hour mark as he was played into the box and fired a shot across goal that was touched behind by Perin.
Pinilla stepped up to take the spot kick, but he saw his effort beaten away by Francesco Bardi.
The Chilean made up for that miss 10 minutes later when he powered in a header to give his side all three points, after Matri had flicked on Diego Perotti's cross.