Scotland are now guaranteed of at least a tenth place finish.
Playing in temperatures of more than 30 degrees Celsius, the Scots started strongly with a try after five minutes from Iain Kennedy which was converted by captain David Blair. Cameron Johnston then scored two before Ben Cairns fired over on the stroke of half-time with Blair adding two more conversions for a 26-0 lead at the break.
Kyle Traynor and Greig Laidlaw added their names to the scoresheet in the third quarter and full-back Colin Goudie celebrated his first match for Scotland U21s with a try in the 60th minute. Georgia were then awarded a penalty try before John Barclay scored in the 72nd minute but the Georgians had the last word adding another converted try in the last move of the game to make it 46-14.
As well as Goudie, Murray Bringhurst and Gregor Wood won their first U21 caps after coming off the bench.
Scotland will now face Fiji to determine ninth and 10th place in the Championship table after the Fijians beat Italy 33-12.
Scotland U21 team manager John Jeffrey said: "It was a good performance but we tired in last twenty minutes. Scoring eight tries at international level is good, but when we were seven tries up at that time, we should have turned the screw.
"Hopefully the win will put juice in tank for the big, strong, fast Fijians who will ask questions of us as they did of Italy."
Scotland team:
Colin Goudie, Cameron Johnston, Ben Cairns, Chris Dunlop, Iain Kennedy (Robert Cairns), David Blair (C) (James King), Greig Laidlaw (Murray Bringhurst), Ryan Grant (Gregor Wood), Kyle Traynor, David Young (Innes Brown), James Eddie (Calum Forrester), Ian Nimmo, Scott Newlands, John Barclay, Alan MacDonald.
Scorers:
5 minutes Iain Kennedy try
David Blair conversion
18 mins Cameron Johnston try
32 mins Cameron Johnston try
David Blair conversion
40 mins Ben Cairns try
42 mins Kyle Traynor try
49 mins Greig Laidlaw try
60 mins Colin Goudie try
Georgia pen try and conversion
72 mins John Barclay try
80 mins Georgia try and conversion
Scotland's fixtures and results:
Friday 9 June Australia 18-14 Scotland Stade Darragon, Vichy
Tuesday 13 June Italy 10-26 Scotland Stade Darragon, Vichy
Saturday 17 June England 31-12 Scotland Stade Emile Pons, Riom
Wed 21 June Scotland 46-14 Georgia Stade Complexe du Mas, Issoire
Sunday 25 June Scotland v Fiji Stade Antonin Chastel, Thiers, kick-off 2.30 local time (1.30 BST)
You can see photos of Scotland's U21 World Cup campaign here