A deflected shot by the veteran midfielder gave the Red Devils the lead after 29 minutes.
Towering defender Tamer Abdul-Wahab brought Contractors level just before the break after converting a right-wing cross.
Egypt skipper Hassan scored three minutes after the restart to restore Ahli's advantage following a neat exchange with Osama Hosni.
Qatari winger Hussein Yasser added a third one minute from time before Contractors striker Ihab Al-Masri, a reported target for Zamalek, notched a consolation deep into stoppage time.
Versatile midfielder Ahmed Fathi played his first pre-season friendly after recovering from a knee injury.
The former Sheffield United man sustained the injury during Egypt's stunning 1-0 victory over Italy in the FIFA Confederations Cup.
Algerian playmaker Amir Sayoud, who will be registered in Ahli's youth ranks, made his debut after coming on as a second-half substitute.
It was the second friendly victory for Ahli following their 2-0 win over Morocco's Wydad Casablanca.
The Red Devils suffered defeats to German side Bayer Leverkusen and Turkish giants Galatasaray.
The Egyptian Premier League holders will face cup winners Hodoud in the season curtain-raiser on July 21st.