Tries from Juan Jose Imhoff, Felipe Contepomi, who added eight points from the boot, and Agustin Gosio saw the Pumas finish second in Pool B behind England and advance to a last-eight clash with hosts New Zealand next weekend.
Scotland needed Georgia to win by eight points or more to advance at Argentina's expense, but Lasha Khmaladze's converted first-half try was all former Scotland head coach Richie Dixon's side could muster.
Argentina, needing just a point to advance as pool runners-up following their 13-12 win over Scotland last weekend, struggled to break through the Georgia defence and Contepomi missed penalties after five and 13 minutes.
But a flowing attacking move saw the Pumas breach the Georgia line after 33 minutes.
Julio Farias' neat inside pass freed Imhoff, who touched down in the corner. Contepomi missed the conversion.
Georgia responded and got beyond the Pumas' defence soon after.
Lekso Gugava's neat chip in-field from the right wing was collected by Khmaladze, who touched down.
Full-back Malkhaz Urjukashvili converted to give Georgia a two-point interval lead.
Argentina exerted continual pressure on the Georgia line early in the second half and Contepomi's first successful kick punished hands in the ruck and put his side one point in front.
Contepomi struck a second penalty after Georgia were penalised following a strong run by Lucas Gonzalez Amorosino, the man who crossed for the match-winning score against Scotland last weekend.
The Pumas skipper then touched down after 68 minutes after finding a hole in the Georgia back line and converted himself to hand his side an 11-point lead.
And it was not to be for Georgia - or Scotland - as the Pumas' class told with a third try one minute from time.
Gosio latched on to Imhoff's grubber kick through to touch down.
Marcelo Bosch added the conversion to complete the win.
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