Heerenveen reach semi-finals
Vitesse went ahead through Stanley Aborah's 41st-minute strike and held that lead until midway through the second half when Viktor Elm levelled for the visitors.
Heerenveen, who defeated second-tier outfit FC Oss 11-1 to reach the quarter-finals, sealed their place in the last four in the 71st minute when Bas Dost fired home.
The quarter-finals continue on Wednesday night when AZ Alkmaar play GVVV Veenendaal and Heracles Almelo entertain RKC Waalwijk, while the action concludes on Thursday when PSV Eindhoven host NEC Nijmegen.