The hosts made a fast start at the Neo GSP Stadium in Nicosia and took the lead in the 19th minute through Leonidas Konomis.
Andronikos Kakoullis doubled Cyprus' advantage in the 31st minute, finishing a move involving Ioannis Pittas to give the hosts a 2-0 lead before half-time.
Cyprus were reduced to 10 men shortly after the restart when Kostas Pileas received a straight red card in the 52nd minute.
Despite playing with a numerical disadvantage for the remainder of the contest, Cyprus protected their two-goal advantage and completed an important home victory.
Armenia controlled 62 per cent of possession and registered nine shots to Cyprus' seven, but the visitors were unable to find a way past the home defence.
The result leaves Cyprus with four points from three matches, while Armenia have three points after the same number of games.
Cyprus will next face Latvia on Monday, while Armenia will travel to Montenegro for their fourth Group C2 fixture.