Using wing-backs Mattia de Sciglio and Alessandro Florenzi to brilliant effect, they were the more potent attacking team until they withdrew in defence of their lead in the final stages.
Giorgio Chiellini scored the game's opening goal, bundling home from close range after David de Gea had parried an Eder free-kick in greasy conditions in the first half.
And Southampton striker Graziano Pelle sealed victory in injury time, volleying home from eight yards after an attempted clearance from substitute Matteo Darmian's cross had looped up invitingly as Italy hit a tiring team on the break.
Italy now face one of the pre-tournament favourites Germany in the quarter-finals. Meanwhile England can join Italy in the last eight by beating Iceland.