The Dark Blue youths fought back from a goal down against their hosts in Korinthos to level through Celtic striker Tony Watt's second-half penalty.
The result will be used as a stepping stone, as the Scots now aim to bounce back from their failure to qualify for this year's finals in Israel by reaching the next tournament, which will be staged in the Czech Republic in two years' time.
The team have been drawn against Holland for the second qualifying campaign running and will also have to overcome Luxembourg, Slovakia and Georgia when their Group Three bid begins next month.
Stark handed debuts to Partick Thistle midfielder Stuart Bannigan and Hearts teenager Callum Tapping, with Stuart Armstrong of Dundee United taking on the captain's armband.
And the Scots almost got off to a flying start as first Sheffield Wednesday midfielder Rhys McCabe was denied just five minutes in by Greek goalkeeper Andreas Gianniotis, while Fraser Kerr failed to bury a header soon after.
The visitors were made to pay for those misses when they fell behind after 13 minutes as the Greeks struck first in front of a 4,000-strong crowd.
FC Amkar Perm striker Nikos Karelis got himself in between Falkirk defender Kieran Duffie and Motherwell youth Kerr at the back post to head the home side in front from Everton forward Apostolos Vellios' cross.
Despite their early dominance, Greece failed to add to their lead as keeper Chris Kettings twice saved from Vellios to leave the deficit at just one goal at the break.
But with 13 minutes of the second period gone, Watt struck his fourth goal in six games for the Under-21s with his spot-kick success.
Kilmarnock teenager Rory McKenzie had been bundled over in the area by Charalambos Lykogiannis and Watt made no mistake from 12 yards as he sent substitute keeper Stefanos Kapino the wrong way.
And yet the hosts still had chances to win it, only to miss four decent opportunities in the space of eight minutes.
First Costas Triandafillopoulos put a header wide from 12 yards just after the hour mark, before Kettings parried again from Giannis Gianniotas and then Panagiotis Ballas.
Then on 69 minutes, Dimitris Kolovos put another strike straight into the keeper's arms as the Blackpool man kept the Greeks at bay almost by himself.
A final chance fell for the home side with five minutes left after Gianniotas had skipped past four challenges, but the Aris forward put his shot wide from 10 yards out.