Greece scored twice in the final 11 minutes after David Targamadze had fired the hosts into a 19th-minute lead.
Substitute Giorgos Fotakis levelled for the 2004 European champions on 79 minutes from long range and surprise call up Charisteas struck five minutes from time in his first international since the 2010 World Cup.
Greece, who finished the group unbeaten in their 10 games, end with 24 points with Croatia second on 22 following their 2-0 home win over Latvia.
Greece are now unbeaten in 16 games since coach Fernando Santos took over from Otto Rehhagel in July 2010.
"These are difficult times for Greece and the Greek people so I hope we have given them something to smile about," said Santos.
"It was a strange game, we didn't start at all well and Georgia scored with their first half-chance of the game. Despite going behind my players kept their composure, we looked for the goal in the right way, by playing our football and creating good opportunities.
"Based on the qualifying campaign I think we have shown that we deserve a place in the finals," Santos added. "I see a team that is improving all the time and maturing together."
Following their 2-0 win over Croatia in Athens on Friday, Greece needed simply to avoid defeat but they fell behind after making a lethargic start.
Dimitris Salpingidis gave a away a cheap free-kick close to the left touch-line with a foul on Levan Mchedlidze and Targamadze whipped over an inswinging dead-ball which curled past keeper Alexandros Tzorvas.
The goal sparked Greece to life, however, and home keeper Nukri Revishvili twice denied the visitors, saving from Kostas Katsouranis and Loukas Vintra.
Greece almost fell 2-0 behind at the start of the second half but left-back Nikos Spiropoulos cleared off the line from a corner.
Santos replaced the labouring Alexandros Tziolis with Fotakis 11 minutes into the second half and the midfielder pulled Greece level, drilling home from 20 yards via a slight deflection off Georgia defender Aleksandr Amisulashvili.
Georgia were down to 10 men by this stage after goal-scorer Targamadze went off injured with 19 minutes left, coach Temuri Ketsbaia having already made three substitutions.
Charisteas, who scored the winning goal in the Euro 2004 final, then put the game to bed in the 85th minute with a clinical low, right-footed finish from just inside the penalty area following an assist from Katsouranis.
The final whistle sparked jubilant scenes among the Greece players who gathered in a circle in the centre of the pitch to celebrate.
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