Jamie Ward and Kyle Lafferty grabbed the goals at Stadio Georgios Karaiskaki as Michael O'Neill's men made it three Group F wins from three, their best start to qualifying for a major tournament.
The contrast between the sides' form coming into the match was stark, with Northern Ireland having beaten Faroe Islands and Hungary while Euro 2004 champions Greece - who reached the last 16 at the recent FIFA World Cup - had picked up just one point from their first two games, against Romania and Finland.
And the pressure felt by new Greece boss Claudio Ranieiri was only added to in the ninth minute as the visitors, brimming with confidence, took the lead.
Ward took the credit, wheeling away in celebration after his effort had struck Loukas Vyntra en route to the corner of the net, before the Ireland man turned provider in the second period for Lafferty to complete a memorable triumph.
Northern Ireland retained their spot at the top the group, with Greece sitting second from bottom, only above the Faroe Islands.
Greece made two alterations to their side, with Georgios Samaras and Kostas Mitroglou coming in for Andreas Samaris and Charalampos Mavrias.
Northern Ireland, whose sole change saw Niall McGinn replaced by Corry Evans, began like a side in good form as they pressed forward.
And that approach brought an opener in the ninth minute when Ward saw a side-footed effort from from Oliver Norwood's corner take a wicked deflection off Vyntra and beat goalkeeper Orestis Karnezis.
A bad night for Vyntra got worse seven minutes later when he was forced off by injury, to be replaced by Kostas Stafylidis.
Having looked nervous at the start, Greece gradually began to grow into the game, with Stefanos Athanasiadis' wild volley their first meaningful effort.
They almost levelled in the 33rd minute when Nikolaos Karelis lobbed a shot over the onrushing Roy Carroll and just wide following fine work from Samaras and Panagiotis Tachtsidis.
But it was Northern Ireland who created the best opportunity over the remainder of the first half, Lafferty brilliantly beating Kostas Manolas before seeing his powerful strike rattle the underside of the crossbar.
The striker made no mistake just after half-time, however, as he finished off a stunning counter-attack.
After Greece had piled on the pressure at the other end, Ward's clearance flew into the path of Lafferty, who brilliantly jinked past Stafylidis and produced a composed finish.
Carroll was pressed into rare action soon afterwards, diving low to his right to keep out Tachtsidis' curler.
However, that effort from range was as good as it got for Greece as they created little over the remainder of the game.