Ajax struck three times to condemn Rangers to six straight defeats in their first Champions League group stage since the 2010-11 season.
Steven Berghuis and Mohamed Kudus scored for the Dutch visitors in the first half.
Kudus thought he scored a second after the restart, but it was ruled out following a VAR check.
With three minutes remaining, James Tavernier converted a penalty for Rangers after Rabbi Matondo was pushed to the ground in the box.
But the visitors restored their two-goal cushion when substitute Francisco Conceicao scored in the 89th minute.
