Levan Kobiashvili struck at the death to give Georgia all three points, with victory leaving Temuri Kestbaia's side just a point adrift of Croatia in UEFA EURO 2012 qualifying Group F.
There were 90 minutes on the clock when Otar Martsvaladze slipped the ball back for Hertha BSC Berlin midfielder Kobiashvili to beat Verdan Runje from ten metres in a game which always looked destined to end in stalemate. Victory means that Georgia remain unbeaten in ten games since Ketsbaia took charge in November 2009.
Croatia did not dominate the early exchanges, but created the first meaningful chance on 28 minutes when Mladen Petrić's quickly taken free-kick drew a save from Nukri Revishvili. The FC Anzhi Makhachkala custodian was called on again after the break, fending Niko Kranjčar's header wide. Kobiashvili then missed the target after getting his head to Aleksandr Iashvili's superb cross from the right.
Zurab Khizanishvili nodded over from another Iashvili delivery, and struck slightly too high soon afterwards, with Gogita Gogua's 78th-minute effort from out on the left meeting a similar fate. However, Kobiashvili's finish ensured his team-mates were left with nothing to regret at the final whistle.