The hosts, playing at the Estadio Algarve, were first to push forward, Joseph Chipolina seeing his effort from outside the box blocked in the sixth minute.
It didn't take long for the higher-ranked visitors to break the deadlock, however, with Giorgi Chanturia's cross in the ninth minute falling to Nikoloz Gelashvili, who duly poked the ball into the bottom corner to put Georgia in the lead.
Georgia carried on bearing down on goal throughout the rest of the first half, with efforts from Chanturia and Gelashvili causing further trouble to the Gibraltarian defence.
Eventually, the game was put to bed by the visitors in the 69th minute when Chanturia set up Jaba Kankava, who duly finished off the move to gift the Georgians a comprehensive victory.
As it stands, Georgia are now fifth in Group D, with the FIFA newcomers at the bottom.