FC Twente beat Eredivisie champions AZ Alkmaar 3-0 to book their place in next season's Champions League.
Kenneth Perez scored the first two minutes after the restart, Peter Wisgerhof made it two on the hour and Eljero Elia sealed the win 12 minutes from time.
AZ also had Gill Swerts sent off shortly after conceding the second goal on a miserable afternoon.
Ten-man Ajax were consigned to a place in the Europa League after suffering a thumping 4-0 defeat at Sparta Rotterdam which ensured the home side's survival.
Edouard Duplan and Yuri Rose put Sparta in the ascendancy with two goals in five minutes just before the interval and, shortly after the 76th-minute dismissal of defender Oleguer, Joshua John and Dele Adeleye struck to seal an emphatic victory.
FC Utrecht twice lost the lead against Feyenoord to leave their own hopes of snatching a Europa League play-off place hanging by a thread.
Tom Caluwe, who had missed a penalty two minutes earlier, gave Utrecht the lead in the 13th minute but Jon Dahl Tomasson equalised.
Mihai Nesu put the hosts in front again shortly after the hour mark before Georgino Wijnaldum secured a share of the spoils for Feyenoord.
PSV paid the price for poor discipline as NEC Nijmegen's Tim Janssen scored in the 90th minute to cancel out Dzako Lazovic's opener. Lazovic and Edison Mendez were sent off for the hosts prior to the equaliser.
Meanwhile, substitute Tim Matavz grabbed the only goal of the game in stoppage-time for Groningen against FC Volendam, having only been on the pitch a minute.
Another late replacement, this time Oussama Assaidi, also decided the match between NAC Breda and De Graafschap, scoring in the 90th minute to hand the visitors three points.
Relegation-battlers ADO Den Haag were denied a vital win after goals from Csaba Horvath (36) and Lex Immers (38) put them two up at Europa League-chasing Heerenveen.
Paulo Henrique (79) and Kristian Bak Nielsen (87) restored parity.
Vitesse Arnhem beat Heracles 1-0 thanks to Lasse Nielson's strike, while a last-gasp effort from Niels Vorthoren e