Giorgio Chiellini pounced after David De Gea pushed out Eder’s free-kick to give the Azzuris the lead in the first half.
De Gea then produced several excellent saves to deny Spain, as they pressed for an equalizer.
Southampton striker, Graziano Pelle, eventually killed off the tie late in the second half with a second goal.
Italy will now play world champions Germany in the last eight on Saturday in Bordeaux.
It's going to be a tough one certainly for the Italians.