Robin van Persie scored a late winner and was then sent off as Feyenoord kept pace with second-placed Ajax in the Eredivisie with a stormy 2-1 win over Vitesse.
PSV emerged handsome winners in the De Topper derby by beating Ajax 3-0 at the Philips Stadion.
Feyenoord lost ground on the leading duo in the Eredivisie as they had to settle for a 1-1 draw at AZ Alkmaar on Sunday.
Ajax climbed into second place behind Eredivisie leaders PSV Eindhoven by thrashing Vitesse Arnhem 4-0 on the road on Sunday.
Fran Sol scored a hat-trick as Willem II thrashed the previously unbeaten Heracles Almelo 5-0 in the Eredivisie.
AZ Alkmaar continued to set a strong early pace in the Eredivisie after overwhelming FC Emmen 4-1 at De Oude Meerdijk.
The 2017 Eredivisie winners Feyenoord were shocked 2-0 by De Graafschap in their first game of the new league season.
Hibernian produced a second-half comeback to seal a 3-2 win against Asteras Tripoli in the first leg of their second round Europa League qualifier on Thursday.
ADO Den Haag and Heerenveen will join Vitesse and Utrecht in the play-offs for the last Europa League spot despite mixed fortunes on the final day.
Former Eredivisie champions FC Twente have been relegated from the league after a thumping 5-0 defeat at Vitesse on Sunday.
Jorrit Hendrix's impressive late strike earned a point for Dutch champions PSV Eindhoven in a 2-2 draw against Roda.
PSV hit back from two goals down to win 3-2 at AZ Alkmaar and extend their lead at the top of Eredivisie to 10 points.
PSV Eindhoven maintained their dominance of the Eredivisie with a 5-1 win over NAC Breda on Saturday.
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Ajax celebrated their 118th birthday in memorable fashion with a 5-2 thrashing of Sparta Rotterdam.
AZ Alkmaar kept the pressure on second-placed Ajax by coming from behind to beat the Eredivisie's bottom club Sparta Rotterdam 2-1.
Steven Bergwijn scored twice as leaders PSV Eindhoven extended their lead to 10 points in a 2-1 comeback victory over bottom side Sparta Rotterdam.
Leaders PSV Eindhoven registered their sixth successive Eredivisie victory as they defeated Excelsior to stay clear of Ajax.
Ajax came from behind to beat NAC Breda 3-1 on Sunday and close the gap on Eredivisie leaders PSV Eindhoven back to seven points.
Feyenoord romped a record derby win over Sparta Rotterdam, stunning their rivals with a 7-0 away success.
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