Having won the game at Cairo stadium, the defending champions closed to within seven points of leaders Petrojet, advancing to the 7th place with 10 points.
Mohamed Barakat broke the deadlock (30), and Ahmed Belal scored a brace in the second half (70), (78).
The petroleum side couldn't cope with the consistent pressure of the five-time African champions, who kept the upper hand throughout the game.
While looking for an opener, The Cairo giants mainly depended on both flanks domination to whip crosses.
Barakat then latched on to Ahmed Belal's deft through to go one-on-one with keeper Nasser Farouk and slot home.
Belal wasted a couple of valuable chances later on.
The misfiring striker could have opened the scoring on the quarter-hour mark when Farouk accidentally flicked the ball towards him, but his reflex wasn't fast enough.
The 28-year-old, whose apt assist helped Barakat tuck in his goal, tried again when he rifled a goal-ward shot which was denied by the keeper.
Ahmed Al-Sayed also couldn't convert a clear-cut opportunity when he failed to connect with Gilberto's corner kick from a point-blank range despite being unmarked.
Asyut's Mashoor Ahmed received his marching order after two bookable offenses, to leave his side more susceptible.
The Red Devils stepped up their efforts to double the lead minutes before the interval, but ended the first half with one goal ahead.
More Pressure
The home side tightened their stranglehold after the interval with more pressure upfront.
Ahli's latest revelation Hani Al-Egeizi was substituted after producing an unimpressive display in the first half.
Belal kept up the fighting spirit to make up for his fans after a mediocre performance in the first half.
The once-superstar managed to score when he slid the ball past Farouk 15 minuets after restart.
He revived his glorious days with a second from a penalty kick to ensure victory over the outnumbered visitors.
The dying minutes witnessed modest attempts from Asyut Petroleum, looking for a consolation goal in vain.