Winger Bencharki made the difference at the Mohamed V Complex in Casablanca, to put his side in the ascendancy ahead of the teams meeting again in Egypt on Saturday.
Zamalek, the five-time African champions, survived an early penalty appeal when Soufiane Rahimi went to ground and wanted a spot-kick.
They nudged in front in the 18th minute, with Zizo's cross from the right perfectly flighted to the far post where Bencharki rose well to head into the net.
Rahimi threatened with a header that almost crept in as Moroccan champions Raja fought back, looking to level the tie.
Youssef Obama then spurned a great second-half chance to give Zamalek a two-goal cushion, seeing his close-range shot charged down.