Goals from Anthony Laffor and Tebogo Langerman, as well as an own-goal from Islam Gamal, put The Brazilians in the driving seat heading to Alexandria for the second leg at the Borg El Arab Stadium next Sunday.
The hosts got off to a better start, keeping possession and maintaining pressure on the Zamalek defence.
The visitors then pushed for a quick response, but some good defensive work saw the likes of Shikabala, Ayman Hefny and Bassem Mosry all fail to threaten Denis Onyango's goal.
Five minutes before half-time, Langerman added a second as his speculative cross-come-shot caught El-Shennawy off his line, with the ball sneaking into the net off the back-post.
Zamalek could have pulled one back when Hefny was allowed space inside the Sundowns box, but his shot sailed narrowly over the crossbar as the half ended at 2-0.
The hosts' lead was further extended just seconds after the restart, when Dolly did well to pick out Tau in space, and the latter's goal-bound shot from an acute angle beat El-Shennawy, before Gamal's attempted block slammed the ball home.
Downs were dealt in blow in the 55th minute, though, as Wayne Arendse was shown a soft yellow card for a foul on Morsy, meaning the defender will miss the second leg due to suspension.
The vistors, however, also had goalkeeper El-Shennawy subbed due to injury shortly after the hour mark, as Mahmoud Abdel Rahim came on in his place.
Zamalek: Ahmed El-Shennawy (Rahim 63'); Moruf Yusuf, Islam Gamal, Ali Gabr, Ahmed Tawfik ; Tarek Hamed, Ibrahim Salah, Ayman Hefny, Shikabala (Ramzy Khaled 56'), Stanley Ohawuchi; Bassem Morsi (Ahmed Fathi 75')