Martin O’Neill’s side knew it was win or bust in Lille, but it looked like a typically spirited display was not going to be enough until Brady popped up to glance Wes Hoolahan’s inch-perfect cross beyond Salvatore Sirigu with five minutes left.
With top spot in the pool already secured and a mouth-watering last-16 tie with Spain on the horizon, Italy boss Antonio Conte made eight alterations to his starting line-up, with the likes of Gianluigi Buffon, Giorgio Chiellini and Antonio Candreva sitting out.
Ireland flew out of the traps in the first half as they attempted to catch Italy’s second string cold.
Despite the largely different personnel, Conte’s side still performed with their usual defensive diligence and Ireland struggled to create clear-cut opportunities.
O’Neill’s team had every right to feel aggrieved for not being awarded a penalty on the stroke of half-time when Federico Bernardeschi barged into James McClean, and Hoolahan should have put them in front when he shot straight at Sirigu from 10 yards.
However, the Norwich City man went from villain to hero, as he sent in a wonderful inswinging delivery for Brady to seal a last-16 meeting with hosts France.