Ciaran Clark’s Republic of Ireland are through to Euro 2016’s last 16.
Martin O'Neill's side knew only a victory would secure a place in the knockout stage in France but had failed to find a way through Italy’s defence until Robbie Brady headed home Wes Hoolahan's cross in the 85th minute.
Clark was on the bench for the encounter in Lyon after starting the previous two games.He and the Irish squad will now face hosts France on Sunday, with a 2pm kick-off.
Meanwhile, Carlos Sanchez and Brad Guzan are both out of the Copa America Centenario after defeats to Argentina and Chile respectively.
Last year's champions Chile were convincing winners in Chicago, although they were made to wait for victory after racing into a two-goal lead, after lightning, heavy rain and the threat of tornados forced the players to stay inside after half-time, while fans took shelter in the stadium.
Charles Aranguiz and Jose Pedro Fuenzalida scored in the first half while Colombia also had to play with 10 men after Sanchez received his second yellow card in the 57th minute.
Guzan was in goal as USA went down 4-0 to Argentina in the other semi-final.
Lionel Messi became Argentina's leading scorer, passing Gabriel Batistuta's 54-goal tally with a 25-yard strike.
Messi provided the assist for Ezequiel Lavezzi's opener, then scored his stunner before Napoli's Gonzalo Higuain fired in to make it 3-0. Higuain scored with a tap-in in the 85th minute to complete the scoring.
USA and Colombia will now face each other in the third-place play-off game on Sunday in Arizona, kick-off 1am.