Theofanis Gekas, the overall top scorer in qualifying with 10 goals, wasted Greece's best chance, while Ruslan Rotan was guilty of poor finishing for the visitors on a night when both sides cancelled each other out at the Olympic Stadium. Sotiris Kyrgiakos almost won the game for Otto Rehhagel's Greece in the dying seconds but the Liverpool defender headed wide.
Both teams began brightly but it was the visitors who threatened first and registered the first shot on target when Alexandros Tzorvas pulled off a comfortable save from Andriy Shevchenko's 25-yard free-kick. Giorgos Karagounis responded for the hosts with a shot from distance which was comfortably held by Andriy Piatov in the Ukraine goal.
Former Chelsea and AC Milan forward Shevchenko then tried his luck again from another free-kick in the 13th minute but his tame effort drifted wide. Greece had the ball in the net after 16 minutes when Gekas turned in Dimitris Salpigidis cross but the assistant referee had already raised his flag for offside.
Rotan wasted a golden opportunity three minutes later after a defensive mix-up from the home side when he dragged his shot wide of the left post from the edge of the box. The visitors continued to look the more dangerous, particularly on the counter attack and Tvorvas was called upon in the 36th minute to make a smart save from Oleg Gusiev's shot from an acute angle.
Greece threatened twice before half-time but striker Giorgos Samaras' control let him down when Salpigidis picked him out with a low centre before Gekas headed straight at Piatov from Karagounis' free-kick. Samaras, who was a peripheral figure in the first half, drew a save from Piatov with a speculative shot from distance as Greece began strongly after the break.
However, again the visitors threatened and Karagounis came to Greece's rescue with a last-ditch tackle to deny Artem Milevskyy in the 55th minute. Tzorvas was called into action again in the 68th minute to push away a rasping Taras Mykhalyk's drive.
Rehhagel then handed 21-year-old striker Kostas Mitroglou his international debut as a replacement for Salpigidis with 19 minutes left as he looked to add attacking impetus to his team. However, the Olympiakos forward failed to make a significant impression and it was Samaras who next went close with a powerful shot which flew just inches over the bar.
Ukraine continued to look dangerous going forward on the break but it was the home side who almost snatched a vital win through Kyrgiakos, but the defender headed Kostas Katsouranis' right-wing cross wide of the left post with only seconds remaining.