Siem de Jong headed home the opener for Ajax five minutes before the break after the Feyenoord defence failed to clear a free kick and 11 minutes into the second half Mounir El Hamdaoui doubled the lead.
Central defender Andre Bahia pulled one back 10 minutes before time for Feyenoord, whose Dutch international Ron Vlaar limped off the pitch with a hamstring injury.
After their 2-1 win Ajax are top with 16 points from six matches, two ahead of PSV and Groningen, who beat Excelsior Rotterdam 2-0 on Saturday.
Champions Twente Enschede slipped to fourth with 12 points after being held 0-0 by 10-man Heracles Almelo, who had Mark-Jan Fledderus sent off on the stroke of halftime for receiving two yellow card within three minutes.
AZ Alkmaar had their first win of the season, beating NEC Nijmegen 1-0 with Brazilian Jonathas on target after 28 minutes, while Utrecht came from behind twice to beat VVV Venlo 3-2 with Ricky van Wolfswinkel scoring a double to lift his season's total to seven.
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