Fernando Santos's team went ahead in the 20th minute through Christodoulopoulos's strike and could have added to the scoreline but for profligacy at the LFF Stadium in Vilnius with striker Dimitris Salpigidis hitting the post in the 89th minute.
Greece have 13 points from six matches and remain three points behind Bosnia who crushed Latvia 5-0 to take their goal tally to a remarkable 23 in six matches.
Bosnia lead the group with 16 points.
Greece looked the most accomplished side for long spells and the winning goal came from a fine move with left-back Jose Holebas crossing perfectly for Bologna forward Christodolopoulos to plant a firm header past diving goalkeeper Emilijus Zubas.
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