"It is rare to see an away team perform this impressively", writes Uefa about the match.
Coach Luciano Spalletti made the sign of the cross and blew a kiss towards the Amsterdam evening sky.
When Khvicha Kvaratskhelia made it 5-1 after weak defensive play in Ajax with half an hour remaining, parts of the crowd got up and went home.
In their first three group stage matches, Napoli have defeated Liverpool 4-1, Rangers 3-0 and now 6-1 against Ajax.
They have a maximum of nine points and 13-2 in goal difference.
"You will probably have to wait a long time for Ajax to be as hopelessly outclassed at home as they were tonight," writes Uefa.
There was a class difference at the Johan Cruijff Arena.
Ajax had nothing to come and also had Dusan Tadic sent off after his second yellow card with 20 minutes remaining.
By then it was already 5-1 so that card had no significance for the outcome.
Napoli thus also set a record – to be the first Italian club to score six away goals in the Champions League.