Brady’s goal arrived just when it looked as if Ireland were heading out due to a combination of Italy goalkeeper Salvatore Sirigu and Romanian referee Ovidiu Hategan.
Before Brady struck, Sirigu, standing in for Gianluigi Buffon in the Italian goal, made a superb save to deny Daryl Murphy while Hategan twice waved away Irish penalty appeals in the first half.
Coach Martin O’Neill made four changes to the side that lost 0-3 to Belgium last weekend in Bordeaux as Ireland looked for their first win over Italy in a competitive match since the 1994 World Cup in the United States.
James McClean and Daryl Murphy started while it was all change in central defence with Richard Keogh and Shane Duffy chosen to partner one another.
The lack of rhythm of what was essentially an Italian ‘B’ team played into the hands of Ireland, who came out of the traps flying, adrenaline pumping and with a vast support behind them.