Feyenoord oust Alkmaar from Dutch Cup
It represented another blow for Alkmaar who also failed to qualify for the knockout stages of the Champions League and are seventh in the Dutch league, 19 points behind leaders Twente Enschede.
Alkmaar sacked coach Ronald Koeman earlier this month, bringing in Dick Advocaat as his successor.
Feyenoord struck four minutes before halftime when Sekou Cisse's shot was blocked by goalkeeper Sergio Romero and Wijnaldum netted the rebound.
Sparta Rotterdam also reached the last eight with a 5-0 victory over amateurs Baronie Breda.
Midfielder Erik Falkenburg opened the scoring midway through the first period before second-half doubles from Kevin Strootman and Charles Dissels completed the rout.
On Monday, second division Go Ahead Eagles Deventer beat top-flight Heracles Almelo 2-0.
Holders Heerenveen host PSV Eindhoven on Wednesday, the same day as Twente entertain second division Helmond Sport and Ajax Amsterdam visit the amateurs of WHC Wezep.