Set on their way by an own goal from Nektarios Alexandrou, second-half goals from Srdjan Lakic and Sebastian Jung gave the Germans their second successive 3-0 victory in Group F, having previously toppled Bordeaux by the same margin.
Coach Armin Veh had warned his Eintracht players to be wary of their hosts, but aside from a dour opening it was a comfortable night for the team that stand 13th in the Bundesliga.
Early strikes for APOEL by Alexandrou, Efstathios Aloneftis and Tiago Gomes carried little threat.
The breakthrough came in the 27th minute when Tranquillo Barnetta sent a raking pass to Jung who took the ball on the volley from the right side of the penalty area, looking to fire a first-time cross to the edge of the six-yard box.
To Eintracht's good fortune, the cross took a wicked deflection off Alexandrou, in close attendance, and the movement left goalkeeper Urko Pardo hopelessly wrong-footed as the ball looped inside the near post.
Centre-back Anderson Bamba headed wide and sent a 25-yard shot at Pardo as Eintracht pushed for a second goal before half-time.
They were kept waiting until the 57th minute, when Vaclav Kadlec fed a neat pass into the path of Lakic and he cracked the ball home beneath Pardo.
Ten minutes later any sense of a contest was over when captain Jung fired the visitors' third, rifling in a 12-yard strike after Johannes Flum played the ball to him from the left flank.
The closest APOEL came was late on when Selim Benachour's 18-yard drive from right of goal was turned aside by Kevin Trapp. They fall a place to third, with one point from two games, while Eintracht head the table by two points from Maccabi Tel-Aviv.