Any other result in Wednesday’s final Group E game at Stade Pierre Mauroy will send the Irish home. And even a win doesn’t guarantee advancement following a 1-1 draw with Sweden and a 3-0 loss to Belgium.
No such worries for Italy, though, as coach Antonio Conte led his team to two straight wins to secure first place in the group.
Belgium could also finish with six points by defeating Sweden, but UEFA rules would still rank Italy higher based on its 2-0 win over the Belgians last week.
Apart from the top two teams in each group, the four best third-place teams will also advance.
In the last 16, Italy will face the runner-up from Group D, likely Croatia or the Czech Republic, in Saint-Denis next Monday.
Participating in a European Championship for the third time after 1988 and 2012, Ireland has yet to make it past the group stage.
Four years ago, Ireland also faced Italy in its final group match but, with zero points from two games, it had already been left without a chance of advancing. Italy won 2-0 and went on to reach the Euro 2012 final.
There is a lot more at stake for Ireland when they face the Azzuri again on Wednesday.
“We’ve got to win this game now against Italy,” Ireland coach Martin O’Neill said after the loss to Belgium. “We feel that if we freshen ourselves up again that we are ready to go.”
Ireland’s last win over Italy in a major competition came at the 1994 World Cup, when an early Ray Houghton goal gave them a 1-0 victory.
Ireland impressed by taking four points from Germany in qualifying for Euro 2016 and will now need to prove again it can keep up with the big teams in Europe.
“We’ve had many fantastic moments against Italy in the past. On Wednesday night, it’s time to do it again. Believe!” the Irish soccer association posted on its Facebook page.
Ireland captain John O’Shea surely believes, saying after the Belgium game: “We have a big chance against Italy.”
The defender, who was expected to start in his 113th game for the national team, said Ireland had performed well despite getting only one point from its first two matches.
“We have to take the positives from the first half (against Belgium) and the game against Sweden as well,” O’Shea said. “And if we do that, with a bit more discipline and control, I think we can get something from Italy.”