Having recently lost out, for the second consecutive year, in their quest for a Champions League spot, APOEL were determined to continue the Isreali champions' woes.
Within 28 minutes of play, the Camels were rattled twice after Nuno Morais' - from the penalty spot - and Cafu handed the visitors a two-goal lead.
Ogu, benefitting off a Nwakaeme assist, halved the deficit in the 42nd minute before the bulky forward intervened in the second half to help his side avoid a home loss.
Beer Sheva, however, failed to capitalise on their numerical advantage after Dellatorre was shown his marching order in the 79th minute.
In what looks like another tough task, Barak Bakhar's men must overturn their first-leg misery in Cyprus on July 16 to avoid missing out entirely on European football this season.