The 25 year-old left winger joined the Cypriot side in July from Brisbane Roar and has started four of their five Champions League qualifiers.
APOEL made the perfect start, Igor Alberto de Camargo scoring off a corner in the second minute, before local boy Efstahios Alonefits doubled the Cypriot side's lead in the tenth minute with a beautiful chip.
Oar was substituted in the 51st minute for Georgios Efrem.
The result puts APOEL in the box seat to qualify for the Champions League group stage which would see them earn upwards of $23 million.
Elsewhere, fellow Aussie Bailey Wright played 90 minutes for Bristol City in their 2-2 draw with Brentford, while James Meredith played 74 minutes in Millwall's 4-3 loss at home to Ipswich Town.
