Eredivisie leaders PSV Eindhoven passed up the chance to establish a five-point advantage as they were held to a 1-1 draw at Heracles Almelo, while champions Ajax slipped further off the pace with a 2-0 defeat at home to FC Utrecht.
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.
Otman Bakkal and Guyon Fernandez were the men on target at the start of each half for the Rotterdammers, who moved up to fifth spot, three points clear of Ajax.
Edouard Duplan netted late in each half to inflict a second straight loss on the injury-hit Amsterdammers and lift Utrecht well clear of the bottom three.
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.