Feyenoord have lost all their away league clashes against the top teams this season and that trend continued in the cup after they allowed PSV to control the match.
After Dries Mertens fired PSV ahead in the 20th minute, Italian Graziano Pelle pounced on a defensive blunder by Atiba Hutchinson to equalise nine minutes later.
But Feyenoord failed to make any further inroads and when keeper Erwin Mulder blocked a shot from Tim Matavz, Van Bommel netted the rebound.
"It is not the first time we conceded a goal from a set piece and this time Stefan de Vrij failed to do his job," Feyenoord manager Ronald Koeman told reporters.
"At moments like that you have to be top and this season in big matches we aren't."
PEC Zwolle came from behind to beat last year's finalist Heracles Almelo 3-2 to reach their first semi-final since 1977.
Marko Vejinovic put Heracles ahead after nine minutes but well executed attacks from Zwolle, finished by Arne Slot and Fred Benson, turned the tide before the interval.
Jesper Drost scored Zwolle's third after 58 minutes before Everton pulled one back.
On Tuesday AZ Alkmaar cruised to a 5-0 win at second division side Den Bosch in a match that was marred by racist chants from the Den Bosch fans in the direction of U.S international Jozy Altidore.
Vitesse Arnhem will host Ajax Amsterdam on Thursday.
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