Gary Haveron's side pushed forward from the first whistle with Matthew Lusty and Ronan Doherty having half chances during the opening encounters.
Despite the Inver Reds dominating possession, it was the away side who thought they taken the lead on 17 minutes through their first chance of the game.
However, Vahid Selimovic's header was ruled out as he was offside, to the relief of the home fans.
As the half progressed, Larne continued to control the game and were denied by Giorgi Makaridze when he made a smart save to collect Sean Graham's effort after a clever counter attack from Lusty.
In the final minutes of the half, Tomas Cosgrove's shot from the back post made Makaridze produce another good save before Rohan Ferguson denied Nikoloz Dadiani's free kick at the other end.
Chances were at a premium after the restart with Doherty unable to keep his effort on target before Lusty's delivery was gathered by the away side's stopper.
The home side pushed until the final whistle, but could not find a way past the away side's resolute defence.