Gertjan Verbeek's side came from behind to dispose of the Eredivisie champions thanks to goals from Maarten Martens, Charlison Benschop and Rasmus Elm.
Siem de Jong put Ajax ahead early on before goals from Maarten Martens and Charlison Benschop reversed the home side’s lead. De Jong netted his second to level matters at half-time but a Rasmus Elm penalty in the second period was enough to send the visitors through to the next round.
Ajax saw the majority of the ball in the opening minutes of the match and were able to open the scoring with its first opportunity through De Jong. Christian Eriksen played a perfectly timed pass over the top of the defence which the Dutch forward brought down with his first touch before slotting past Esteban Alvarado to put Ajax ahead after 10 minutes.
AZ immediately applied pressure as the club looked to draw level and came close moments after conceding when Simon Poulsen went on a surging run down the left flank, beating Ruben Ligeon and then cutting back for Brett Holman, but the Australia international hit the post.
The away side maintained the pressure and its persistence paid off as it found the equalizer when Benschop latched onto a through ball down the right wing and whipped it into the box for the incoming Martens, who was able to smash it home.
Gertjan Verbeek’s side continued to attack the Ajax goal and took the lead in 32 minutes. Elm played a fantastic through ball to put Benschop one-on-one with Jasper Cillessen and the striker coolly slotted it past the goalkeeper and into the bottom corner.
Ajax pulled itself level five minutes later when Vurnon Anita played a short free kick to Eriksen. The young Dane galloped forward before lining up a shot which was saved by Esteban but the keeper could only parry it into the path of De Jong, who tapped it home with ease to level the sides at the break.
AZ immediately went on the attack in the second half and regained the lead in the 55th minute. A Beerens shot from outside the box struck the hand of Toby Alderweireld and the referee was quick to point to the spot and Elm stepped up and placed it into the bottom corner.
Frank de Boer’s side pressed in search of a way back into the match but AZ held onto their lead and progressed to the next round.