O'Neill's men go into their third Group F fixture on Tuesday off the back of two wins, having beaten Hungary and the Faroe Islands in recent weeks, while the hosts have just a point to their name.
Claudio Ranieri has yet to taste victory in his first international role, although Greece did get up and running courtesy of a 1-1 draw in Finland on Saturday.
Jarkko Hurme's equaliser denied Greece three points in Helsinki and Ranieri will hope home advantage can serve his side well when O'Neill's table-toppers visit the Stadio Georgios Karaiskakis.
The Northern Ireland boss feels his side have given themselves a platform to build on, as they seek to qualify for their first European Championship, and urged his side to make the most of their momentum.
"The campaign is about momentum and getting into the group as soon as possible, and that's what we've managed to do," he said after Saturday's win over the Faroe Islands.
"Now we go into the next two fixtures with everything to gain. They are going to be very difficult games, away in Greece and away in Romania.
"But equally we've put ourselves in a position with everything to gain based on the first two results."
Greece have won all three of their home matches against Northern Ireland, with their most recent meeting likely to bring back positive memories for the home side.
In October 2003, the sides were goalless in their final Euro 2004 qualifier at the Stadio Apostolos Nikolaidis and, with Spain winning in Armenia, the Greeks were heading for the lottery of the play-offs.
Vassilios Tsiartas then scored the winning goal from the penalty spot to ensure Greece's place at the competition in Portugal.
Guided by Otto Rehhagel, the hugely unfancied Greeks went on to produce one of the biggest international shocks ever by lifting the trophy in Lisbon.
As Ranieri seeks his first win in charge, the former Monaco coach feels it would be a "disaster" if they failed to qualify for the competition in France two years from now.
"Our goal is to qualify. I said from the first day, if we don't qualify, it is a disaster - for me, for everybody," he said.
"It was important to get the first point, now we have to think about the next match."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.