The Irish win, when combined with Belgium's 1-0 victory over Sweden in the night's other Group E clash, also dashed Turkish hopes of qualifying for the last 16.
In the first half Ireland were a team transformed for the one which slumped to a miserable 3-0 defeat to Belgium on Saturday. The men in green needed a win to make it through to the last 16, whereas Italy – who made no less than eight changes to their starting lineup – were already assured of a place.
Ireland started strongly and a number of attempts by players like Jeff Hendrick – whose 9th-minute effort when just wide – and Daryl Murphy's header, could have paid off.
Although Italy dominated possession in the first half, it was the Irish – backed by a chorus of green-clad passionate fans – who looked more intent on scoring, knowing that nothing less than a win would do.
At the end of the first half Martin O'Neill's men were left furious when Derryman James McClean was bundled over in the penalty box, but Romanian referee Ovidiu Hategan was unmoved.
In the second half, Italy looked brighter, with the new starters playing for team places in the last 16. However, Ireland showed their scoring intent, with Seamus Coleman's 57th-minute shot forcing a save from Italian 'keeper Salvatore Sirigu.
Ireland's intensity in the second half began to take its toll, with O'Neill taking off Murphy for Aiden McGeady in the 70th minute. Ireland's Wes Hoolahan, who scored in the 1-1 opening draw against Sweden came on in the 77th minute and was joined later by veteran striker Robbie Keane as the Irish pressed for a goal.
Robbie Brady's dramatic 85th-minute header sent the Irish fans and manager O'Neill into a frenzy and the Irishmen held on to secure a historic victory – the side's best competitive win over Italy since the 1994 World Cup.