The entertaining clash had finished 2-2 after extra time but that was nothing compared to Vitesse Arnhem's 10-1 hammering of third-tier amateurs ADO '20 Heemskerk.
Graziano Pelle put Feyenoord ahead after 28 minutes with a well-executed volley but 10 minutes after the break Jeffrey Gouweleeuw equalised.
"It is always a pleasure to be decisive in a shootout but we caused our own problems," said Feyenoord keeper Erwin Mulder, who saved four penalties.
"After our second goal we should have sealed the match and then we again concede a goal from a set piece," he added.
Last season's runners-up Heracles Almelo had to come from behind to beat NAC Breda 3-1.
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