Namibia lost inspirational skipper Jacques Burger to concussion in the 10th minute and somehow led 6-0 at halftime - despite missing 33 tackles - thanks to two Theuns Kotze penalties.
But Gorgodze crossed for a try early in the second-half to settle nerves, while Lasha Malaguradze also crossed for a try and Merab Kvirikashvili kicking two conversions and a penalty.
Kotze ensured a tight finish with a third penalty and his own converted try with five minutes to play.
Ill-discipline undid Georgia in the opening half, former Toulouse hooker Jaba Bregvadze yellow-carded in the 34th minute after smashing his elbow into the face of replacement back Heinrich Smit.
And then came 11 minutes of extra-time after Georgia kicked for touch, lost their ball, but won it back. A series of scrums followed, with predictably Namibia prop Raoul Larson and then his replacement Johannes Coetzee both yellow-carded, Gorgodze pleading for a penalty try.
It was all set up for Georgia to score, but from an uncontested scrum, Gorgodze's pass inside to Kolelishvili was adjudged to be forward and Namibia could breathe again after leading at half-time of a World Cup match for the first time.
Stripped of their scrum dominance, Georgia opened the second period with the ball in hand.
Despite a number of errors, the ball was finally worked to Gorgodze, the Toulon No.8 powering over for a welcome try.
Referee George Clancy dished out a third yellow card to Namibia, sending Bothma to the bin for a chokehold tackled on Malaguradze, the fly-half promptly crossing for a second try following a fine Gorgodze charge and offload.
Kvirikashvili nailed the two conversions and a 65th minute penalty to pull Georgia out to 17-6 before Kotze kicked his third penalty.
It was not over, however, as a woeful clearance kick by replacement forward Lasha Lomidze was recycled and worked to Kotze who dived in at the corner, nailing the touchline conversion with aplomb to make for a nervy run-in.
Georgia 17 (Mamuka Gordgoze, Lasha Malaguradze tries; Merab Kvirikashvili 2 conversions, penalty), Namibia 16 (Theuns Kotze try, conversion, 3 penalties). HT: 0-6
-AFP
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