Ghanaian ace Bekoe opened the scoring on 28 minutes, before Osama Mohamed earned Mokhtar Mokhtar's men a two-goal cushion.
Ahmed Eid pulled one back for Hodoud seven minutes from the hour mark, but Bekoe killed off the game with a third strike three minutes from time.
Egypt U-20 man Islam Ramdan received his marching orders late in the game for his harsh challenge on Petrojet's Walid Soliman.
Now Petrojet are on top of the league table on 17 points, several goals ahead of defending champions Ahli who will regain their three-point lead if they beat ENPPI later in the day.
Early Penalty
Hodoud could have taken the lead only in the first minute when the referee pointed at the spot after Ahmed Safi was felled in the area by Osama Mohamed as both players were racing for the ball, but Ahmed Abdul-Ghani's effort hit the crossbar.
Harras remained in charge during the early minutes of the match.
Abdul-Ghani tried to atone for squandering a penalty-kick with a powerful long-range shot, but the keeper was up to scratch.
On the quarter-hour mark, Petrojet had their first scoring opportunity when Ahmed Shaban tried his luck from distance, but guardian Mathurin Kameni blocked his fierce drive.
Walid Soliman incredibly ran half the length of the field amid three challengers, to go one-on-one with the keeper but a muscle cramp resulted in a poor finish.
The Petroleum side were fired ahead when Bekoe hit a spectacular opener from 25 years, when he caught out the advanced keeper with a sublime volley.
Mohamed, who awarded Hodoud a penalty, made amends and doubled Petrojet's lead.
He latched onto a Bekoe deft pass to beat the offside trap and sprinted down the left flank till he penetrated the box and chipped with style over the goalie, who once again was away from his goal.
After the break, Hodoud stepped onto the pitch with an obvious intention of canceling out their opponents' two-goal lead.
The Alexandrian outfit got the upper hand in terms of ball possession and chances, while the hosts were a bit dangerous on the counter attack.
Ahmed Eid wasted a golden chance to reduce the arrears when he tried unmarked to net from close range, but the crossbar denied his shot.
Seconds later Abdul-Ghani scored the home side's sole goal from a narrow angle with a clinical finish that went off the bar and into the net, to become the league top scorer with six goals.
Hodoud maintained their onslaught afterwards, with Petrojet relatively losing their coherence.
Eid tried to notch an equalizer with a low shot from outside the area, but the ball went yards past the post.
Islam Ramdan was sent off for knocking down the running Walid Soliman in the area on 87 minutes; second bookable offence.
Bekoe completed a brace upon converting the late spot kick.
The match's goals