PSV Eindhoven missed out on the opportunity to establish a five-point lead at the top of the Eredivisie with a 1-1 draw at Heracles Almelo.
With FC Twente and AZ Alkmaar seeing their games postponed, Fred Rutten's men were seeking a win to put more space between them and their title rivals.
It looked like they were going to get it when Zakaria Labyad gave them the lead in the 19th minute, but Everton's 76th-minute equaliser meant PSV had to settle for a draw.
Injury-hit Ajax slipped further out of the Eredivisie title reckoning as they slumped to a 2-0 defeat at home to FC Utrecht.
Edouard Duplan scored late in each half to inflict a second straight defeat on the champions and move the visitors well clear of the bottom three.
It was incredibly Utrecht's fourth league win over the Amsterdammers in the past two seasons, and it left Ajax with a mountain to climb if they are to defend their crown.
Feyenoord climbed above Ajax in the Eredivisie standings with a 2-0 victory at NEC Nijmegen.
Otman Bakkal and Guyon Fernandez were the men on target at the start of each half for the visitors. The win moved the Rotterdammers up to fifth spot - three points clear of their arch rivals following the champions' defeat.
Finally, RKC Waalwijk were impressive 3-0 winners at FC Groningen. The visitors were two up within five minutes thanks to Rick Ten Voorde's penalty and Petter Andersson's own goal, and sealed the points in the 64th minute through Guy Ramos' strike.