Chadli scored either side of a Luc Castaignos effort as the visitors turned up the heat on their title rivals.
Belgium international Chadli broke the deadlock two minutes into the second half before Castaignos made it two 15 minutes from time, running onto a through-ball into the area before finishing coolly.
Chadli added a third seven minutes later with a 20-yard chip which left goalkeeper Esteban Alvarado stranded.
The win put Steve McClaren's side three points clear of PSV Eindhoven, with Ajax a point further back in third, although both sides have a game in hand.
AZ remained in 12th place.