Namibia, meanwhile, gained their first ever point in the Rugby World Cup after finishing just a point behind their opponents in Exeter.
Theuns Kotze kicked through the posts to give Namibia the lead after just two minutes when Georgia came in offside.
The fly-half then had a chance to double their lead after five minutes but a drop-goal missed the posts.
Georgia then attacked the Namibia try-line but a penalty was called and the African team were able to clear.
Kotze added three more points after 18 minutes from in front of the posts after the Georgians were penalised for a high tackle.
The ball went over the line once again, but the TMO decided that there was a forward pass in the build up and Namibia held on for the half-time lead.
It took just five minutes for Georgia to add a second try when Lasha Malaguradze crossed after Georgia won a lineout inside the 22 of Namibia.
Georgia's dominance of the second half continued when Kvirikashvili added three more points to the total from a penalty.
Namibia had not given up hope though, and Kotze pulled three points back from a penalty.
The Namibia talisman then took his team to within a point of their opponents, and broke his nation's scoring record, by going over on the left wing and converting his own try. It was too late for Namibia though, as the Georgians held on to a narrow victory.
Georgia's qualification for the 2019 Rugby World Cup will be confirmed if Tonga fail to beat New Zealand on Friday.body check tags ::