كتب : Hatem Maher
Mohamed Al-Herda scored the winner seven minutes after the restart following a dreadful blunder by the keeper.
The midfielder's low shot squirmed beneath the custodian's body to break Bayelsa's resistance.
Hodoud, who were missing striker Ahmed Salama due to injury, survived an early scare before laying siege to the visitors' area.
The Alexandria-based club tried their luck from distance more than once through Ahmed Eid and Abdul-Salam Nagah but their shots went wide.
They could have taken the lead after 33 minutes but Bayelsa keeper parried two successive close-range shots from Egypt duo Eid and Ahmed Abdul-Ghani.
Hodoud moved top of Group B on three points. Mali's Stade Malien will meet Angolan side Primeiro de Agosto in the other group game on Saturday.
The Egyptian Cup winners will face league champions Ahli in the local Super Cup on Tuesday.