Feyenoord and Roda JC secured opening day victories in the Eredivisie.
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
After the title was taken away from them on Saturday, Ajax were held by struggling NAC Breda at home on Sunday.
Feyenoord moved a step closer to qualifying for the Europa League after a 2-2 draw at Willem II Tilburg in the Eredivisie.
Ajax lost more ground on Eredivisie leaders PSV Eindhoven after they were held to a 1-1 draw by Utrecht.
It was a day to forget for Utrecht defender Ramon Leeuwin as he scored an own goal and was sent off against Ajax.
Cash-strapped Twente Enschede returned to winning ways in the Eredivisie on Saturday with a 2-0 win over PEC Zwolle.
Ajax staged a late rally to beat PSV Eindhoven 3-1 on Sunday to give their faint title hopes a boost.
Ricardo Kishna struck twice as Ajax beat Twente 4-2 in the Eredivisie to cut PSV's Eredivisie lead back to 12 points.
Stefan Nijland scored in each half as PEC Zwolle moved up to third with a thumping 4-0 win at bottom side Dordrecht.
Ajax lost 1-0 at Vitesse Arnhem on Sunday to fall further behind PSV in the Eredivisie title race.
Feyenoord beat FC Twente to strengthen their hold of third place in the Eredivisie on Sunday, while Heerenveen won at Utrecht.
PEC Zwolle moved up to fifth in the Eredivisie as they beat ADO Den Haag 3-1 and FC Twente drew 2-2 against Vitesse.
FC Utrecht condemned struggling NAC Breda to a fourth consecutive Eredivisie defeat with a 5-1 thrashing on Saturday.
Eredivisie leaders PSV Eindhoven could only draw at FC Groningen on Sunday, while FC Twente beat PEC Zwolle to go third.
Excelsior striker Carlo de Reuver came off the bench to snatch a last-gasp 2-2 draw against FC Utrecht.
PSV restored their cushion at the top of the Eredivisie after a 5-1 win over Utrecht, as Feyenoord nudged up to third.
PEC Zwolle lost ground on the Eredivisie's leading pack with a 3-2 defeat away to Go Ahead Eagles.