After 15 minutes of action at the Tottenham Hotspur Stadium, Ziyech assisted Donny van de Beek in scoring the only goal that separated both teams in the encounter.
The contribution took the playmaker's tally to 18 assists across all competitions this season.
Ziyech was later replaced by Klaas Huntelaar in the 87th minute while compatriot Mazraoui was introduced for Lasse Schone in the 65th minute as the Dutch giants held on to a crucial win in North London.
Onana's saves between the sticks were also crucial as Ajax kept a clean slate and a goal advantage.
Kenya's Wanyama was in action for the entire 90 minutes for Spurs but his contribution from the middle of the park was not enough to save them from defeat.
The Premier League side will look to bounce back from the defeat when they visit Amsterdam for the return fixture next Wednesday.
Wanyama is expected to lead Kenya's charge for their maiden Afcon title in Egypt.