Ajax finished a remarkable title-winning season with a 14th consecutive Eredivisie win while Excelsior's relegation was confirmed on the final day of the regular season.
The champions needed late goals from defenders Andre Ooijer - the 37-year-old playing his last ever game - and Jan Vertonghen to secure a 3-1 win at Vitesse Arnhem.
Nicky Hofs had threatened to end Ajax's impressive run when he opened the scoring on 28 minutes, but a 41st-minute Dmitri Bulykin leveller paved the way for their late rally.
At the other end of the table Excelsior slumped into the Jupiler League with a 3-1 defeat to PSV Eindhoven.
Excelsior's fleeting hopes were quickly dashed as goals from Dries Mertens (10) and Jeremain Lens (37) left them in a hole they were unable to extricate themselves from.
Luigi Bruins did reply on 50 minutes from the penalty spot but after Zakaria Labyad (66) added a third, and closest rivals De Graafschap beat ADO Den Haag 5-3, Excelsior's fate was sealed.
De Graafschap came from behind three times, Charlton Vicento's opener quickly cancelled out by Aleksandar Radosavljevic's own goal before Lex Immers and Michael de Leeuw twice traded goals.
Gil Vermouth and Soufian El Hassnaoui then earned the visitors victory.
PSV's win was not enough for them to snatch the second Champions League place though as Feyenoord ensured a return to Europe's premier club competition with a 3-2 win at Heerenveen.
Heerenveen, who qualified for the Europa League despite defeat, had led through the prolific Bas Dost, but the Rotterdam club responded with goals from Otman Bakkal, Sekou Cisse and Elvis Manu.
Rajiv van la Parra netted Heerenveen's second.
AZ Alkmaar, already qualified for the Europa League, ended their campaign with a 1-0 home win over Groningen.
Erik Falkenburg scored the only goal on 26 minutes.
Twente and RKC Waalwijk joined Vitesse in the Europa League play-offs despite failing to win on Sunday.
NEC Nijmegen are also through after a 2-1 win at Heracles Almelo.
Twente lost 4-2 at VVV-Venlo to give them a timely boost ahead of their relegation play-offs after late goals from Steven Berghuis and Michael Uchebo.
The contest sprang to life after the first half-hour when both teams traded goals from Leroy Fer (31) and Yanic Wildschut (45).
Nacer Chadli fired Twente ahead again on 48 minutes but VVV came roaring back as Danny Holla (61) equalised before the late goals.
RKC went through following an entertaining 3-3 draw at NAC Breda.
RKC took the lead through Rick ten Voorde but NAC established a 3-1 lead just after the hour mark thanks to goals by Alex Schalk, Omer Bayram and Robbert Schilder.
But RKC hit back for a point, levelling through Aaron Meijers and Sander Duits.
NEC scored in each half through Lasse Schone and Genero Zeefuik in their win over Heracles, who replied through Everton.
That meant they jumped ahead of Roda JC, who lost at home to FC Utrecht 3-1.
Alexander Gerndt put the visitors in front on the stroke of half-time following poor goalkeeping from Mateusz Prus.
Yoshiaki Takagi doubled the away side's lead four minutes after the break and, even though Sanharib Malki pulled one back, Frank Demouge sealed a win for Utrecht late on.