
The Azzurri had secured a berth to next June's continental tournament already Saturday with a 2-1 win at Scotland and retained first place in Group B ahead of France, also previously qualified before Ukraine.
An opening own goal from Frodi Benjaminsen on 10 minutes made things easy for Italy, who secured their ninth win out of 12 qualifiers through efforts from Luca Toni, Giorgio Chiellini.
The guests' goalkeeper Jakup Mikkelsen managed a great save on 16 minutes, slapping wide a header from Toni, but stood no chance 20 minutes later when the striker fired home from inside the area after controlling a Vincenzo Iaquinta assist.
It was the fifth goal in the qualifying phase from the powerful Bayern Munich striker, who was born in a town not far from Modena.
Mikkelsen was stunned again on 41 minutes as young defender Giorgio Chiellini scored his first goal for the Azzurri drilling a smashing left-footed shot by the far post.
Suni Olsen on 43 minutes fired narrowly above the bar and came close again on 50 minutes with a free kick well controlled by Marco Amelia, who kept goal allowing a game off to star Gianluigi Buffon.
A high header from Iaquinta opened a second half that saw Italy hold the upper hand as Raffaele Palladino and Toni had their shots saved on 62 and 67 minutes.
The Faroes, however, pulled one back on 83 minutes through a good header from Rogvi Jacobsen, who had threatened with another header five minutes earlier.
Jacobsen, who scored all of his side's four goals in the qualifiers, was on target against Italy also in the 2-1 defeat suffered in the home leg.
A good chance for the guests' second goal went begging with one minute left as Johan Davidsen nodded against the post.
"I saw a great participation from the public. I am happy for this people who saw the team close the qualification with a good result," said Italy coach Roberto Donadoni, who quelled rumours of a possible contract renewal with the Italian football federation (FIGC).
"I am not thinking about renewing my contract. I do mind about it now. It doesn't matter to me and it should not matter to anyone else."