The prolific forward opened the scoring after 20 minutes when he capitalised on a mistake from Chievo keeper Christian Puggioni to tap home.
© AP Photos
There was nothing fortunate about his second before the break, a stunning volley at the far post to smash in from a tight angle.
The visitors threw on Luciano and got forward in numbers, but were unable to find an equaliser.
Cyril Thereau carried the biggest threat of a late leveller, but his efforts were kept out by a determined defence that held firm in the closing stages.
Di Natale was again instrumental as the home side added shine to the scoreline late on, providing the corner for Morrocan Mehdi Benatia to volley home and wrap up all three points for Francesco Guidolin's men.