Kolbeinn Sigthorsson opened the scoring after eight minutes and substitute Danny Hoesen made it two after 72 minutes as they finished seven points ahead of PSV Eindhoven.
PSV were beaten 3-1 at FC Twente on the final day and had Mark Van Bommel sent off for good measure. Luc Castaignos put Twente ahead after three minutes and Nacer Chadli added a second.
Dries Mertens pulled one back with a penalty five minutes before the break, but Willem Janssen re-established the two-goal cushion in the 54th minute and PSV's misery was complete when they lost Van Bommel in the 71st minute.
A 59th minute goal by Graziano Pelle was enough for Feyenoord to beat NAC Breda 1-0 leaving them level on points with PSV, but they missed out on the Champions League on goal difference.
Fourth-placed Vitesse Arnhem completed what has largely been an excellent season with a disappointing 1-0 home loss to VVV-Venlo, who finished in the relegation play-offs, despite Brian Linssen goal after 27 minutes.
Roda JC will also head into the play-offs for the right to play in the top flight next term on the back of a win as Krisztian Nemeth's 31st-minute goal gave them a 1-0 victory at home to Heerenveen.
Bottom side Willem II bowed out of the Eredivisie with a 2-0 win over AZ Alkmaar as a Virgil Misidjan effort and a Giliano Wijnaldum own goal earned them a 2-0 success.
Fifth-placed FC Utrecht won 3-0 at home to Heracles Almelo thanks to three second-half goals.
Cedric van der Gun opened the scoring after 54 minutes and Jacob Mulenga made it two from the penalty spot in the 71st minute after Heracles had had Jason Davidson sent off. Jens Toornstra completed the scoring three minutes later.
PEC Zwolle were 4-2 winners at home to ADO Den Haag with Fred Benson on target twice either side of half-time.
ADO then had Charlton Vicento sent off on the hour mark only to get one back through Santi Kolk five minutes later.
But Mustafa Saymak got a third for PEC two minutes later and, even though Rydell Poepon pulled a second back for ADO five minutes from time, Youness Mokhtar netted at the other end a minute later to make it 4-2.
RKC Waalwijk won 2-1 at NEC Nijmegen.Goals in each half from Kenny Anderson and Florian Jozefzoon put the visitors in command before Kevin Conboy's last-minute consolation.