Fiji scored six of their seven tries after half-time to secure a vital bonus point win, with man of the match Semi Radradra scoring twice and setting up three other tries.
Coach John McKee said the whole squad was determined to make amends after last week's defeat against Uruguay.
"Our boys were bitterly disappointed and they really wanted to make a statement today," McKee said.
"They're very proud in representing their country and it means a lot for them representing the Flying Fijians and deep down they just wanted to express themselves as rugby players today and it's so pleasing that we managed to do that."
McKee was particularly pleased with how Fiji's scrum managed to get the upper-hand over the much-vaunted Georgian pack.
"Probably the first year I was coaching the Flying Fijians and pre November-tour we met with them for some opposed training in Toulouse and they really dusted us up in the scrum, we were nowhere near in the contest," he said.
"That's the work that's gone in over four or five years that we've got to where we are today and our scrum matches anyone in the world. You saw today that we've got good depth as well - players come into the game and maintain the standard."
Georgia coach Milton Haig said his side could not contain Fiji's firepower out wide in the second half.
"Once you let Fiji get in behind you and they put a couple of passes together it's very difficult to defend and you can just see as soon as they made the line break they get very excited about support play and always having somebody (to pass to), it's a little bit like sevens," Haig said.
"We know they're the best in the world at doing that and where we defended really, really well and were scrambling really well in the first half, our energy and execution in defence just wasn't quite there in the last 30 minutes of the second half."
The Flying Fijians made 19 clean breaks and broke 41 tackles during the match. Centre Waisea Nayacalevu, who scored the opening try, said their success out wide was the result of a lot of hard work.
"Because we trained that during the week, we executed very well during the game and very happy about the result... I think because before the game we agreed that we bring our A-games and we tries to stick on that... I think it just clicked today, the combinations and moves and the execution," Nayacalevu said.
Fiji winger Josua Tuisova was fortunate to avoid sanction for a high tackle late in the first half, which appeared to deny the Lelos winger Alexander Todua a crucial try.
"(I was) a bit worried. I thought they were going to send me but I thought they were just going to give me the warning because I just throw my hand and then release quickly as well... because there was two in one and I tried to control myself for both of them just hit them one by one. I wanted to leave one and follow the ball to hit the other one," Tuisova said.
Haig said the tackle was an important moment in the first half.
"It looked clearly on the replay that it was around the head and he was the last defender so you turn that around and even if it was five points (had he scored or) it could have been seven points in terms of the conversion, but in the context of the first half absolutely, you end up going in with points ahead (if a penalty try had been awarded). Would it have changed the match? I'm not sure," Haig said.
"In the long run, the second half, how the Fijians played it was either seven or eight tries to one... maybe they ended getting their tails up and the score is the score."
Georgia conceded 13 penalties in the match and number eight Beka Saginadze accused officials of allowing Fiji to get away with a lot of infringements.
"Any other team would be punished really, really, really badly so would have finished the game with 13 (players) or any numbers because the tackles they made and the cleanouts they made.
"I think (the referees) need to open their eyes widely about it and while we take all the responsibility - it's really sad that we lost with that difference - but if they would give any of the cards, even yellow or red card, we might have seen another match in the second half," Saginadze said.
Fiji's first win of the World Cup lifts them temporarily to second place in Pool D, two points behind their next opponents Wales.
After rediscovering their Fijian flair, McKee said his side could give the Six Nations champions a run for their money on Wednesday.
"I think they've shown a bit more in attack in the World Cup, they've shown a bit more willingness to play with the football, so they're a dangerous team and it's a big challenge for us next week," McKee said.
"But we've got a good team as well so we'll approach the game in a very positive manner. We will know the areas that we need to counter and if we can take our advantages in the game and turn our opportunities into points I think it will be game on."