Sierra Leone winger Jonathan Morsay scored the only goal for the home side, his second of the campaign, but was not enough as the visitors took home maximum points.
The visitors took the lead in the 24th minute through Miguel Ángel Guerrero Martín from the penalty spot before Sergio Castel Martínez doubled their lead two minutes later.
Morsay, 25, reduced the deficit in the 52nd minute to lift his side. However, Anorthosis showed more composure to score their third in the 92nd minute via Ousseynou Thioune as they wrapped up the victory.
As a result, the home team succumbed to back-to-back defeats and sat eighth on the league standings.
APOEL vs. Ethnikos Achnas and AEZ hosting Paphos FC. will end matchday six of the Cyprus first league on October 2nd.