The opening goal in Doetinchem came after 14 minutes. Gregory van der Wiel crossed in from the right wing and Uruguayan Luis Suarez headed home for 1-0.
The striker added his second four minutes before the break, finding the target from a free kick.
And another free kick would give Ajax the chance to add a third as Urby Emanuelson sent an effort past the opposing goalkeeper in the 68th minute.
Ajax continued to dominate and Suarez completed his hat-trick after combining with Demy de Zeeuw in the 85th minute. Another four minutes later, a low drive from Christian Eriksen set the score to 0-5.