Georgia striker Levan Mchedlidze, who, along with goalkeeper Giorgi Makaridze and Levan Kenia, was one of three 17-year-olds making their first start for his country, headed the home side in to the lead after 16 minutes.
Scotland were denied a decent penalty claimed before the interval when James McFadden was brought down by Georgia captain Zurab Khizanishvili - but when David Siradze drilled home number two in the 65th minute, it stifled any prospect of a comeback.
Scotland boss Alex McLeish tried to be upbeat as he said: "We're disappointed but we are still in the picture and we go into the last game with a wonderful chance - and we know we can do it.
"The whole nation should be behind the team. Everyone should be proud of what this set-up has achieved through Walter Smith before me and, of course, the players.
"They've bounced back before. We know we are playing the world champions and we've said all along that Italy and France are the favourites.
"But the Italians have to come to Glasgow and we have to win the match."
McLeish, like most of the Scotland camp and all of the Tartan army inside the Boris Paichadze national stadium, believes referee Knut Kirkher denied the visitors a clear penalty when McFadden went tumbling inside the Georgia box.
He said: "We finished the first half strongly. I felt we should have had a penalty.
"If we had got that and scored that would have changed the complexion of the game.
"I've been told by the BBC that it was a stonewall penalty.
"But Georgia didn't surprise me, I knew they had some good skills. I don't take anything away from Georgia, they played a good game."