Giergio Chiellini pounced to open the score in the first half before Graziano Pelle secured the win late on, sending the Azzurri through to the quarter-finals of the competition
Spain's defence of their European title has come to an end at the round-of-16 stage after they suffered a 2-0 defeat to Italy on Monday.
The Euro 2008 and 2012 winners were seen as one of the favourites to win the tournament again this year, but were sent home thanks to goals from Giorginio Chiellini and Graziano Pelle.