Decked out in green, a colour they had worn just once before at the Stadio Olimpico back in 1954, Roberto Mancini's new-look Azzurri pushed their perfect run in Group J to seven games for a maximum 21 points.
Despite being pegged back by the Greeks for over an hour the Italians confirmed their dominance and are now assured of finishing top of the group.
Chelsea midfielder Jorginho slotted in a penalty after 63 minutes in the Italian capital with Juventus forward Federico Bernardeschi scoring the second goal on 78 minutes.
“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,” said Mancini.
Italy are one of 12 host nations for Euro 2020 with the opening match to be staged at the 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.
“We hope that they will return,” said Mancini, “and that in June it will be even more beautiful.”
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,” said the 54-year-old former Italy international.
“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.”