Both teams passed up good chances to score but it was the visitors who created the most opportunities and they will have the advantage in Wednesday's return leg in Donetsk.
Theofanis Gekas passed up Greece's best chance with a first-half header while Ruslan Rotan was guilty of missing Ukraine's clearest opening when he dragged a shot wide.
"We now have a slight advantage because we are playing at home," Ukraine coach Olexiy Mikhailichenko told reporters.
"We tried to play on the counter attack and our game plan was effective. We now have to sit down and analyse the game to see how we will approach the return."
Both sides looked lively in the opening exchanges and it was the visitors who registered the first shot on target when Greek goalkeeper Alexandros Tzorvas stopped Andriy Shevchenko's low free kick from 25 metres.
Shevchenko tried his luck again from another free kick in the 13th minute but his tame strike drifted wide.
FLAGGED OFFSIDE
Gekas, who scored 10 goals in qualifying, had the ball in the net when he converted Dimitris Salpigidis's cross only to be flagged offside.
Greece threatened twice before halftime but Giorgos Samaras's control let him down from a Salpigidis centre and Gekas headed straight at Pyatov from a free kick.
Karagounis then had to come to Greece's rescue with a saving tackle to deny Artem Milevskiy.
The 21-year-old Olympiakos Piraeus player showed some good touches but it was Samaras who went close with 10 minutes left, firing just over the bar before Kyrgiakos's late miss.
"Ukraine were very effective with their passing combinations and their attacking players were very good," said German Rehhagel.
"If we had conceded a goal it would have made things extremely difficult for us. I think we scored a perfectly valid goal but the referee disallowed it and we are disappointed."
