Emanuelson put Ajax ahead early in the second half when he found his way through the home side's defence after collecting a Miralem Sulejmani pass but Moussa Kalisse equalised in the 80th minute with a shot from a tight angle to force extra time.
Ajax were then reduced to 10 men when their Spanish player Gabri received his second booking five minutes from time but scarped a last-gasp win when Emanuelson grabbed his second goal.
Feyenoord overcame second division visitors Den Bosch 2-0 while holders Heerenveen and last year's runners-up Twente Enschede cruised to home wins of 4-2 and 3-0 respectively over second division RBC Roosendaal and amateurs Capelle.
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