The Morocco international scored his third goal in three games in the tournament this season but was not enough to hand Erik ten Hag’s men a first-leg advantage with Marco Asensio’s scoring a late winner.
The Sons of the Gods started the game unimpressively after Karim Benzema put the visitors in front at the hour-mark.
The 25-year-old then levelled procedure for the Dutch side in the 75th minute, firing home from David Neres’ cross.
With three minutes left to play Marco Asensio scored the winning goal to deny Ajax a share of spoils in the encounter.
Ziyech featured for the entire duration of the game alongside his compatriot Noussair Mazraoui.
The former Heerenveen winger has now scored 15 goals in all competitions this season and will hope to continue the sparkling performance when his side take on NAC Breda in their next league game on Sunday.