Hodoud trailed 2-1 from the first leg but secured an emphatic victory in Alexandria to go through with a 6-3 aggregate win.
Abdul-Ghani, who would have been forced to play as a keeper if Ali Farag had sustained an injury or received a red card due to lack of goalkeeping options on the bench, was very effective upfront.
He scored three goals and his strike partner Ahmed Mekki notched twice to lift Hodoud past Simba, whose only goal came through Emmanuel Okwi.
Tarek Al-Ashri's side will book a place in the group stage if they win their next two-legged tie against an opponent who is yet to be determined.
They will face one of the teams who will bow out from the Champions League round of 16.
Early Initiative
Hodoud needed two minutes to grab the initiative and overturn the first-leg deficit.
Egyptian international forward Ahmed Eid, one of Hodoud's most consistent performers, superbly eluded a challenger on the left before exchanging passes with a teammate on the edge of the area.
He sent in a low cross that was diverted into the net by Mekki on the second attempt after his initial close-range effort was blocked by Simba keeper.
Hodoud looked on course for a comfortable victory when Abdul-Ghani doubled their advantage on 12 minutes with a low shot from inside the area after a goal-mouth scramble.
But Simba, who had earlier gone close with a low shot from Juma Jabu, threatened to ruin their night with a 37th-minute goal.
They were awarded a penalty after diminutive left-back Mohamed Mekki, who said Zamalek are interested in signing him in the summer, unintentionally handled a cross after needlessly waving his arm.
Okwi stepped up to convert the penalty and level the aggregate score.
However, another penalty, this time at the other end, gifted Hodoud a third goal on the stroke of halftime.
Abdul-Ghani sent the keeper the wrong way after being tripped by Jabu inside the area.
Hodoud, who lie seventh in the Egyptian Premier League table, ran riot in the second half to put the result beyond doubt.
Mekki added the fourth on the hour mark with a free header that went under the body of the keeper and into the net.
Towering striker Abdul-Ghani, Hodoud's top scorer in the league with nine goals, completed his hat-trick 13 minutes from time with a delightful curling shot to wrap up the convincing win.