Right-back Gregory van der Wiel put Ajax ahead with a fierce drive after nine minutes before U.S forward Jozy Altidore struck twice in three minutes early in the second half.
Feyenoord opened with a 1-0 win at Utrecht as Sekou Cisse headed the winner six minutes before the interval.
Former England manager Steve McClaren's Twente Enschede cruised to a 4-1 home win over Groningen with Serb Dusan Tadic scoring twice against his old club and setting up the other two for Nacer Chadli.
Marco van Basten's return to the Dutch league as a coach after a three-year absence ended with his Heereveen side losing 2-0 at home to NEC Nijmegen.
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