Fernando Santos' side controlled proceedings from the kick-off and went ahead in the first half through central defender Kyriakos Papadopoulos' header.
Greece missed two penalties in the second half with Celtic striker Giorgas Samaras and Panathinaikos midfielder Kostas Katsouranis both seeing their efforts saved by the impressive Armenia keeper Roman Berezovsky.
Santos gave a first start to 19-year-old midfielder Kostas Fortunis in place of the rested Sotris Ninis, and the Kaiserslautern player pressed his claim with a series of direct runs and intelligent passing.
As was the case with the 1-1 draw with Slovenia four days earlier, Greece again showed promising glimpses of their attacking game in patches while always remaining solid in defence.
Dimitris Sapigidis went close to opening the scoring for Greece in the 10th minute with a downward header from captain Giorgos Karagounis left-wing free-kick which bounced over the bar.
After an uneventful spell of play, Greece then took the lead in the 23rd minute when Schalke defender Papadopoulos rose unmarked to head home a Karagounis free-kick which was lofted into the penalty area by the Panathinaikos midfelder.
Striker Fanis Gekas then narrowly missed adding a second when he was centimetres away from connecting with a Salpigidis cross on the half-hour mark before then seeing a shot cleared off the line by an Armenian defender.
Berezovsky ensured the scoreline stayed at just 1-0 when he brilliantly pushed a Karagounis long range strike round the post just before halftime.
Greece goalkeeper Michalis Sifakis was called into action for the first time in the match when he made a fine low save from Gevorg Ghazaryan's snap shot three minutes into the second half.
But it was Greece who should have added to the scoreline.
Substitute Samaras, who replaced Fortunis at half-time, won a penalty 19 minutes from full-time after being fouled by Sargis Hovsepyan but his poor side-footed effort was gathered comfortably by Berezovsky.
Substitute Giannis Fetfatzidis was then felled in the penalty area by Artak Yedigaryan four minutes from time as he weaved his way between defenders but again Berezovsky came to the rescue to save from Katsouranis.
Greece face co-hosts Poland in the opening game of the championship on June 8.
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