The hosts fell behind in the 66th minute when Michalis Konstantinou put Cyprus ahead but Levan Kobiashvili equalised seven minutes later to give Georgia their first point in Group Eight.
Cyprus were arguably the better side and will feel aggrieved not have claimed a much-needed win which could have come their way had Konstantinou converted a 53rd-minute penalty.
Having been forced to play their previous ‘home’ qualifier against the Republic of Ireland in the German city of Mainz, Hector Cuper’s Georgia would have been desperate to reward their fans with a win.
But with FIFA president Sepp Blatter watching on from the stands in a show of support, they were unable to get the better of a Cyprus team on the up.
Following a goalless opening period, the visitors passed up a wonderful chance to open the scoring when home keeper Giorgi Lomaia saved a Konstantinou spot-kick awarded when Zurab Khizanishvili brought down Efstathios Aloneftis.
But Cyprus overcame that setback by taking the lead shortly after, a swift counter-attack led by Aloneftis culminating in Konstantinou cutting inside to curl a shot past Lomaia.
But their joy was shortlived as Schalke midfielder Kobiashvili capitalised on being afforded too much time and space to chest down a loose ball and fire into the bottom corner.
The result leaves both sides with just one point so far, although Cyprus have played two games compared to Georgia’s three.
GEORGIA: Giorgi Lomaia, Ucha Lobzhanidze, Lasha Salukvadze, Giorgi Shashiashvili, Levan Kenia (Beka Gotsiridze, 64), Alexander Iashvili, Levan Mchelidze (Rati Aleksidze, 75), Zurab Khizanishvili, Luka Razmadze, Levan Kobiashvili, Zurab Mentesashvili.
CYPRUS: Antonis Giorgallidi, Chrysostomos Michail (Marios Nikolaou, 37), Konstantinos Makridis, Elias Charalambous, Andreas Constantinou, Efstathios Aloneftis (Georgios Panagi, 90) Marios Ilia (Lambros Lambrou, 82), Ioannis Okkas, Konstantinos Charalampidis, Michael Konstantinou, Alexandros Garpozis.