Fernando Santos' side faced going to the finals in disarray after failing to win in any of their four previous friendlies, including a disappointing 1-1 draw against Slovenia in Kufstein last Saturday.
The early strike from Papadopoulos will have restored confidence in the Greek side, who begin their finals campaign against hosts Poland in the opening match next Friday.
Greece could have won by more but missed two second-half penalties, Armenia keeper Roman Berezovsky saving spot-kicks from Georgios Samaras (70) and Kostas Katsouranis (86).
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