WATCH: High-flying Celtic humbled by holder Real Madrid
Edson Alvarez, Steven Berghuis and Mohammed Kudus were all on target inside 33 minutes, with that Ajax's earliest three-goal lead in the competition's history.
Rangers, also beaten 4-0 by rivals Celtic at the weekend, made a triple substitution at the break but Ajax showed no remorse and added a late fourth through Steven Bergwijn.
Ajax was dominant from the first whistle and there was a sense of inevitably about their opener when an unmarked Alvarez headed in Dusan Tadic's in-swinging corner.
Berghuis added a somewhat fortunate second for Ajax, the Netherlands winger's strike taking a big deflection off James Sands on its way past Jon McLaughlin.
A quickfire third followed as Kudus was allowed to charge into the box and fire a stunning shot across McLaughlin and into the top-far corner.
Rangers had a Borna Barisic strike chalked off for offside, and Ajax only added to their opponents' pain thanks to Bergwijn's finish following a terrible pass from Ryan Jack.