Dries Mertens put PSV ahead after five minutes but 10 minutes later Nick van der Velden equalised from close range after a chip from Lasse Schone was cleared off the line by Marcelo.
Tim Matavz restored the lead for PSV four minutes before the interval after good play by Ola Toivonen and Kevin Strootman, who added a third minutes later.
Nijmegen, who had other good chances, hit back through a long drive from Schone in first-half stoppage-time but could not grab an equaliser in a comparatively dull second period.
On Wednesday AZ Alkmaar and Heracles Almelo reached the semi-finals after home wins over the amateurs of GVVV Veenendaal and RKC Waalwijk respectively, while Heerenveen beat Vitesse Arnhem 2-1 on Tuesday in their last-eight clash.
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