If New Zealand beat Tonga in Newcastle tomorrow, then Georgia will qualify automatically for the 2019 tournament in Japan by finishing third in Pool C after their 17-16 win at Sandy Park.
Theuns Kotze kicked two penalties to give Namibia a half-time lead — their first in 18 World Cup matches.
Georgia, who were denied two tries in a first half which took more than an hour to complete, made the breakthrough through their own talisman Gorgodze.
The Europeans pummelled Namibia up front before Gorgodze crashed over from close range.
Malaguradze ghosted through for a second try after a bullocking run and a fine offload by Giorgi Tkhilaishvili.
Kvirikashvili kicked a penalty to extend Georgia’s advantage to 11 points with 12 minutes remaining.
Kotze added a second-half penalty, try, and touchline conversion to set up a frantic finale.
However, Georgia held on for a triumph that was built on forward supremacy.
Tries: Kotze. Cons: Kotze. Pens: Kotze 3.
Botha, Philander, D. van Wyk, de la Harpe, R. van Wyk, Kotze, Jantjies, Redelinghuys, van Jaarsveld, Larson, van Lill, Uanivi, Burger, du Plessis, Bothma, Coetzee.
Smit for D. van Wyk (28), Tromp for de la Harpe (76), Stevens for Jantjies (67), Engels for Redelinghuys (59), Coetzee for Larson (59), Kitshoff for Burger (10), Conradie for du Plessis (59), van der Westhuizen for Coetzee (71).
Tries: Gorgodze, Malaguradze. Cons: Kvirikashvili 2. Pens: Kvirikashvili.
Kvirikashvili, Mchedlidze, Kacharava, Sharikadze, Todua, Malaguradze, Lobzhanidze, Nariashvili, Bregvadze, Zirakashvili, Nemsadze, Mikautadze, Tkhilaishvili, Kolelishvili, Gorgodze.
Tsiklauri for Kvirikashvili (75), Aptsiauri for Mchedlidze (43), Begadze for Lobzhanidze (65), Asieshvili for Nariashvili (35), Mamukashvilli for Bregvadze (56), Datunashvili for Mikautadze (56), Lomidze for Kolelishvili (41).
George Clancy (IRFU).