AZ claim a Europa League place at the expense of Feyenoord, who were consigned to the play-offs for a place in Europe.
NAC Breda face a relegation play-off, while Manchester United-bound Memphis Depay scored for PSV.
PSV came from behind to extend their lead at the top of the Eredivisie standings, while there were wins for Heracles and Utrecht
Feyenoord moved a step closer to qualifying for the Europa League after a 2-2 draw at Willem II Tilburg in the Eredivisie.
Five-star PSV close in on Dutch title after comprehensive victory at FC Twente, while Heracles grab dramatic late win
Markus Henriksen netted a late winner as AZ strengthened their grip on fourth place with a 2-1 win over Cambuur Leeuwarden.
Cash-strapped Twente Enschede returned to winning ways in the Eredivisie on Saturday with a 2-0 win over PEC Zwolle.
FC Twente recovered from 2-0 down to draw 2-2 at Willem II as both teams saw their fading European hopes take another hit.
AZ Alkmaar had to overcame blustery conditions to beat Willem II 2-0 to reclaim third place in the Eredivisie on Saturday.
Feyenoord slipped 20 points behind leaders PSV in Eredivisie after a 2-0 defeat at lowly Heracles on Saturday.
Stefan Nijland scored in each half as PEC Zwolle moved up to third with a thumping 4-0 win at bottom side Dordrecht.
PSV as they scored twice in the last six minutes to defeat Willem II 2-1 on Saturday and extend their Eredivisie lead.
Feyenoord beat FC Twente to strengthen their hold of third place in the Eredivisie on Sunday, while Heerenveen won at Utrecht.
The first half of the Eredivisie season concluded with wins for Ajax and Feyenoord, but with PSV hold a four-point lead.
There were wins for the Eredivisie's leading sides on Saturday night - and plenty of goals along the way.
PEC Zwolle claimed a 2-0 win over FC Groningen in the Eredivisie on Saturday, while ADO Den Haag beat Willem II 3-2.
Ajax bounced back from their defeat in Barcelona by beating Go Ahead Eagles in the Dutch Eredivisie, while Willem II won at Heracles
PSV Eindhoven strengthened their hold at the top of the Eredivisie as they beat AZ Alkmaar and saw Ajax held by Twente.
Heracles claimed their first win of the Eredivisie season with a 6-1 rout of NAC Breda, while Cambuur climbed to fourth.
PSV Eindhoven missed the chance to move three points clear at the top of the Eredivisie as they lost 1-0 at Heerenveen.