It was an unforgettable return to the competition for Rangers as they were picked apart by the hosts.
Edson Alvarez opened the scoring in the 17th minute before Steven Berghuis added the second goal just after the half-hour mark.
A minute later, Mohammed Kudus increased Ajax's lead to 3-0 going into the break.
Super Eagles defender Calvin Bassey made his Champions League debut for Ajax, and he marked it with an assist for his team's third goal and also helped them keep a clean sheet.
Calvin Bassey joined Ajax from Rangers in the summer after spending spending two years in Scotland
Steven Bergwijn put the icing on the cake with ten minutes to go to hand Ajax a comfortable win and the maximum points.
Up Next for Ajax in the Champions League is a trip to Liverpool on September 13, while Rangers will welcome Napoli to the Ibrox Stadium on the same day.
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