After a 1-1 draw in the first leg, the Egyptian side produced a fine display in front of their home fans and moved ahead thanks to Mohamed Abou Trika's 54th-minute strike.
The 35-year-old midfielder controlled a loose ball inside the penalty area and fired beyond Senzo Meyiwa for his fifth goal of the tournament.
Ahmed Abdul Zaher made sure of victory with a second goal in the 78th minute, while Sherif Abdul Fadil was given a late red card for two bookable offences.
Al Ahly missed three chances in the opening half, but the visitors still had opportunities at the other end.
The deadlock was broken when a shot from Abdalla El-Said deflected off a defender's legs and dropped to Abou Trika, who controlled the ball and calmly converted a low shot.
The Pirates went close just after the hour through Luyanda Bacela, but he could only fire into the side-netting from a tight angle after rounding the goalkeeper.
Al Ahly then sealed victory as Abdul Zaher latched on to a mis-hit shot from El-Said and tapped home for his third goal of the competition.
With seven minutes remaining the hosts were reduced to 10 men due to Abdul Fadil receiving his second yellow card of the match, but they were able to hang on.
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