Nigerian striker Henry Akile and veteran defender Ateya Saber also scored for the home side while Ramie Rabie and Reda Al-Weeshi found the net for Arab Contractors.
Both sides now have nine points each, and are placed sixth and seventh in the table, with Arab Contractors leading on goal difference.
The guests grabbed a surprising lead in the sixth minute, with Rabie slotting home from the rebound after Ehab Al-Masri's shot was parried.
Asyut leveled after just five minutes, with Akile lofting the ball smartly over keeper Mohamed Al-Akabawy from inside the area.
In the 27th minute, spot-kick specialist Saber stepped up to deliver a penalty into the back of the net as Asyut took the lead.
Arab Contractors manager Mohamed Radwan fielded Reda Al-Weeshi for Rabie and the former Ahli striker came close twice.
He hit the woodwork from inside the area before Asyut keeper Naser Farouk blocked his powerful shot.
Al-Weeshi made up for the squandered chances when he poked past Naser Farouk, who parried a Tamer Abdul-Wahab shot into his path.
Cameroonian defender Vintal grabbed the three points just two minutes from time when he connected with an inch-perfect cross and headed home.