Despite being pegged back by the Greeks for over an hour, Roberto Mancini’s new-look Azzurri confirmed their dominance and are now assured of finishing top of the group.
Brazilian-born midfielder Jorginho converted a penalty after the hour mark after a blatant handball by Andreas Bouchalakis.
Then substitute Federico Bernardeschi scored from outside the area with a low, bouncing shot that was deflected.
“I want to thank the fans at the Olimpico for supporting us, even in the first half when we were not brilliant, maybe a little nervous at being back in Rome,” Mancini said.
Italy are one of 12 host nations for Euro 2020 with the opening match to be staged at Rome’s Stadio Olimpico.
And Mancini said he hoped that four-time world champions Italy could relive the “magical nights” of the 1990 World Cup in Rome.
Italy will play at least two of their pool matches in Rome next June.
Mancini has rebuilt Italy since their stunning failure to qualify for Russia 2018 and they reached Euro 2020 with a record three games to spare.
“I’m happy and proud to have helped this team get out of a complicated situation,” he said.
“We’ve managed to create a team in a short space of time.
“It wasn’t easy but we have to thank the players who quickly adapted to each other.
“It’s a team with character, who play with pride, never give up and fight until the end, but who still need to improve.
“We have a lot of work, but we’re not far off the best European teams.”