Uruguay was coming off an upset win over Fiji on Wednesday and didn't have the energy to match the physical Georgian lineup, which was overhauled after an opening loss to Wales and raced out to an early lead.
Jaba Bregvadze, who plays for the Japan-based Sunwolves in Super Rugby and was leading his national team for the first time, secured a bonus point with Georgia's fourth try when he dived across from a rolling maul in the 52nd minute.
The Georgians had nothing going on in attack six minutes later when the veteran hooker, standing one out from a ruck, decided to chip ahead and then pinned Uruguayan Rodrigo Silva on the tryline, allowing centre Giorgi Kveseladze the easiest of tries.
Tedo Abzhandadze converted to make it 33-7 before the hour mark, the Georgians having added three tries after leading 12-7 at the halftime break. Tries through left winger Alexander Todua and No 8 Otari Giorgadze in the first half-hour saw Georgia appear to be on the verge of taking control of the game, before Uruguay rallied with a try against the run of play in the 33rd minute.
That was to be their only points as Georgia claimed their first win of the tournament.
The Georgians will have to regroup quickly for a crucial game against Fiji on Thursday, while Uruguay gets an extra two days off before taking on two-time champion Australia.
Georgia 33 (Alexander Todua, Otari Giorgadze, Levan Chilachava, Jaba Bregvadze, Giorgi Kveseladze tries; Tedo Abzhandadze 4 conversions)
Uruguay 7 (Andres Vilaseca try; Felipe Berchesi conversion)
HT: 12-7
