The African outfit were in control throughout in a performance that should keep spirits high going into the World Cup, which begins in 12 days time.
All of Algeria's goals came in the first half, defender Essaid Belkalem putting them in front early with a scrappy close-range finish.
Nabil Ghilas then doubled the advantage before Islam Slimani effectively made sure of victory with Algeria's third.
Striker Artur Sarkisov did reduce the arrears in the second half, however, Armenia never looked like mounting a comeback as Algeria cruised to a straightforward success.
Algeria face Romania on Wednesday before travelling to Brazil to face Belgium, Russia and South Korea in Group H.
Vahid Halilhodzic's men made a strong start at the game in Sion, Switzerland and were rewarded after 13 minutes when Belkalem bundled the ball home from a corner.
Armenia responded well but were punished for failing to test Algeria goalkeeper Mohamed Zemmamouche after 22 minutes as Ghilas struck.
The Porto striker rattled an effort in off the crossbar following a superb run and pass from midfielder Riyad Mahrez.
And the game was put beyond doubt four minutes before the break as Sporting Lisbon striker Slimani displayed great reactions, nodding in from point-blank range after Ghilas had headed against the crossbar.
Two minutes into the second half Armenia gave themselves hope, Sarkisov capitalising on a defensive lapse from Algeria.
He raced onto a backpass following a miscommunication in the Algerian backline before slotting into the bottom corner.
Algeria did have a chance to restore their three-goal lead late on as substitute El Arbi Hillel Soudani cleverly worked his way to edge of the area, only to be denied by a strong save from Armenia goalkeeper Roman Berezovskiy.
But that proved to be little more than a footnote as Algeria sealed a strong result as they prepare to try and reach the last-16 of a World Cup for the first time.
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