The Belgian champions secured their place in the semis with a 7-0 aggregate victory after winning the first-leg 1-0.
Egypt skipper Hassan set-up Max Von Schlebrügge for the opener in the 21st minute before Argentinean Nicolas Frutos doubled the lead from the spot two minutes after restart.
The in-form Hassan added the third two minutes later with a brilliant looping shot from 40 yards over the advancing keeper.
Congolese striker Mohamed Tchite bagged a brace in the 78th and 80th minutes and Hassan completed the rout three minutes from time with a close-range shot.
Genk played the entire second-half with 10 men on the field after Sinan Bolat was sent-off one minute after the interval.
Hassan, who joined Anderlecht from Turkish side Besiktas in the off-season, netted 14 goals in all competitions.