APOEL, in the group stage after losing their Champions League playoff to Astana, started brightly but it was the visitors who nearly broke the deadlock early on when Max Meyer rattled the crossbar from 25 yards.
Andre Breitenreiter's side finally got the goal that they deserved just before the half-hour mark when Matip beat goalkeeper Boy Waterman to Geis's free kick to flick a header home for his second goal in as many games.
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That advantage was doubled just seven minutes later as the German side's leading scorer Huntelaar drilled a low shot past Waterman from 30 yards, but only a point-blank stop from Ralf Fahrmann prevented Piero Sotiriou getting APOEL back into the game on the stroke of half time.
Schalke continued in the same vein after the restart and wrapped up the victory with 20 minutes remaining when Huntelaar grabbed his second with a clinical finish from Meyer's pass.
Things got worse for the Cypriot champions when Tomas de Vincenti was sent off with 12 minutes remaining, but by then the damage had already been done as Schalke started their return to the Europa League after three consecutive Champions League seasons with a well-deserved three points.