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The hosts soon started to dominate the possession and broke the deadlock with just under half-an-hour gone when Shaun Maloney fired a volley towards goal, resulting in the keeper punching the ball onto Khubatia's legs and into the back of the net.
Naismith and Maloney continued to put the Georgia keeper under pressure as half time approached, but Loria did enough to prevent Gordon Strachan's men from doubling their lead before the break.
Steven Fletcher and Naismith continued to combine well and trouble the Georgia defence in the second half, but the former drifted offside while attempting to force another save out of a busy Loria.
However, an error from Hanley let Gelashvili in for an attempt to get the visitors back on level terms, but his effort flew well high of the crossbar.
Valeri Kazaishvili tried to create something with a quick counter-attack, but Maloney got back to help out the defenders and prevent the winger from getting a shot away.
Irakli Dzaria had Georgia's best opportunity to equalise, but the substitute pulled his volley wide after being set up by Gebashvili, allowing Scotland to hold on for the victory and their first Group D points of the campaign.