كتب : Hatem Maher
The Egypt international forward broke the deadlock early in the first-half before adding the second 12 minutes past the hour mark with a superb individual effort.
Amr Zaki came off the bench in the second-period to wrap up the win four minutes from time.
Mansoura finished the game with nine men on the field after Ahmed Omran was sent-off in the 55th minute and Rashad Farouk followed him on the sidelines in the 77th minute, both for second bookable offenses.
The Cairo giants will face relegated club Asyut Petroleum in the semi-final after the latter defeated ENPPI 2-1.
Zamalek dominated the entire first-half as Mansoura couldn't impose a single threat until the half-time whistle blew.
Skipper Hazem Emam had the first chance for the hosts after three minutes when he superbly put the ball between a defender's legs and went clear on goal but his poor shot was easily collected by the keeper.
Hamza opened the score line six minutes later after he controlled Abdul-Halim Ali's brilliant chip pass inside the area before drilling a left-footed shot that took a deflection and went into the roof of the net.
The talented forward could have doubled the lead in the 19th minute when he was released by Emam's neat pass but his close-range shot went inches wide of the post.
In the 26th minute, Mansoura midfielder Islam Abdullah fired a powerful long-range drive that went over the bar.
Hamza widened Mansoura's misery in the 72nd minute when he raced through the opponents' midfield before unleashing an unstoppable bullet that went into the top corner of the net.
Zamalek's top scorer this season Zaki completed the rout four minutes before the final whistle when he capitalized on a defensive mix-up to slot home past the advancing keeper.