Amr Zaki, Hazem Emam, Mostafa Gaafar and Tarek Al-Sayed were on the score sheet to help Zamalek, who didn't feature in last year's edition, edge closer to the Champions League round of 32.
The return-leg will be played in Burundi on the 11th of February.
Zamalek needed just three minutes to open the score line when Zaki cut ahead of the keeper to head home Ahmed Ghanem's inch-perfect cross from the right flank.
The Egypt international striker almost doubled the lead in the 11th minute after he poked home from close range but the goal was ruled out for an alleged handball. Television replays showed that Zaki controlled the ball on his chest.
Two minutes later, the prolific Zaki received Ghanem's cross at the far post and fired a powerful drive that cannoned off the crossbar.
Zamalek kept on dominating possession and threatened on several occasions while Vital'O failed to create any scoring opportunity.
Emam extended the lead three minutes before the interval when he scored a rare header into the top corner of the net after being set-up by Al-Sayed's corner.
Gaafar added the third three minutes past the hour mark after he converted Zaki's miscued shot into the back of the net from close range.
In the 73rd minute, Emam sent a superb lob that was denied by the bar before being replaced by Youssef Hamdi amid standing ovation from the home crowd who enjoyed their favorite man's display.
Al-Sayed put the icing on the cake shortly after when he raced down the left-flank before sending a cross which deflected off a defender and went into the back of the net.
While Zamalek were celebrating their huge victory, a defensive mix-up resulted in the visitors' only goal seven minutes from time.