Ajax boss Erik ten Hag said: "Compliments to the team. They were hungry -- 13-0, a very good victory indeed, a new record. VVV has shown this season that they are capable of getting good results, we've seen that this season already, but it is our accomplishment. We have forced this ourselves."
Venlo were reduced to 10 men on 52 minutes when Christian Kum was sent off after the video assistant referee upgraded his yellow card for violent conduct to a red.
However, the damage had already been done at this stage, with Ajax 4-0 up thanks to two goals from Traore and additional scores from Ekkelenkamp and Dusan Tadic.
Venlo further collapsed after the sending off with four Ajax goals in five minutes from Traore, Anthony, Ekkelenkamp and Daley Blind.
Traore added his fourth on 54 minutes, and two goals from Klaas-Jan Huntelaar on 74 and 76 minutes took it to 11-0.
With 12 minutes left, Lisandro Martinez made it 12-0 before Traore added his fifth of the game on 87 minutes.
VVV Venlo boss Hans de Koning said: "I really don't have much to say. A total off day. We had too much respect for Ajax. We have it made too easy. We have failed. But no one passed away today. It is a match. We have lost. And it is a historic loss, but we need to take it as a man. Head up, chest out."
The previous record for biggest scoreline in the Eredivisie was also held by Ajax, who beat Vitesse 12-1 in 1972.