A brace from Hazem Emam in addition to goals from Gamal Hamza, Mahmoud Abdul-Razeq 'Shikabala', Wael Al-Qabani, Abdul-Halim Ali, Mostafa Gaafar and Ahmed Ghanem led Zamalek to a huge win.
The Cairo giants will face either Mansoura or Arab Contractors, who face each other on Tuesday.
Zamalek were ahead in the 25th minute when Hamza laid off the ball to Shikabala, who hit a left-footed shot into the right bottom corner of the net.
Hamza turned from provider to scorer nine minutes later when he connected with Shikabala's corner at the near post to head the ball into the back of the net.
Left-back Osama Hassan added the third three minutes before the break after he sidestepped a defender on the edge of the area before drilling a low shot past the hapless keeper.
Unmarked Ali widened Bany Sweif's misery seven minutes after re-start after receiving Hassan's cross from the left-flank with a close-range header into the net.
Skipper Emam was introduced and he made an impact shortly after, scoring the fourth three minutes past the hour mark with a curling shot from the edge of the area.
Defender Al-Qabani put his name in the score sheet from the penalty spot in the 69th minute after Hamza was brought down inside the area.
Emam was on target again three minutes later with a very simple header after being set-up by another pinpoint cross from Hassan.
Right-back Ghanem notched the eighth in the 78th minute with a right-footed shot from a tight angle before Gaafar completed the rout five minutes from time.