The Red Devils, who are aiming to complete the double after winning a sixth consecutive league title, found no difficulty in brushing aside their weak opponents.
A brace from striker Mohamed Fadl, who played on his own upfront due to shortage of options, and a goal from substitute Ahmed Shokri lifted Ahli, who won the cup a record 35 times, to the next round.
They will face Zamalek, who claimed a narrow 1-0 victory over Fayoum earlier in the day, for the third time this season.
Their first league meeting this season ended goalless while the second ended in a 3-3 draw.
Playmaker Mohamed Abou-Treika, who is struggling to regain top form after recovering from a serious foot injury in February, wasted an early chance to put Ahli in front but Fadl made amends on 30 minutes.
Attacking midfielder Ahmed Hassan intercepted a poor pass from Nabaroh defender Mahmoud Bakr and crossed for the unmarked Fadl inside the area to send a low right-footed shot into the bottom corner.
Mohamed Barakat, who scored Ahli's last-gasp equalizer in the 2-2 Cairo derby draw with Zamalek last month, limped off injured in the second half.
It remains to be seen whether he will be able to take part in Wednesday's anticipated clash against the White Knights.
He made way for youngster Shokri, who established himself as a key Ahli player after being promoted to the first team by coach Hossam Al-Badri this season.
Fadl doubled Ahli's advantage nine minutes after the restart with a superb volley after capitalizing on a poor defensive clearance.
Shokri completed the rout on 74 minutes with a simple header after Nabaroh keeper failed to handle a tame cross from Ahli right-back Ahmed Ali.