Christian Eriksen put Ajax ahead on 12 minutes after finishing off a fine pass from Ryan Babel, however the lead was short lived as Feyenoord's 18-year old debutant Jean Paul Boetius equalised from a tight angle 11 minutes later.
Siem de Jong restored the visitors' lead shortly after the restart but Feyenoord wrestled control from Ajax once defender Niklas Moisander was given his marching orders in the 75th minute.
Pelle's equaliser right at the death was almost followed by an injury-time winner but the 27-year-old striker was denied by a superb save from goalkeeper Kenneth Vermeer.
After 10 games, champions Ajax remain fourth in the Dutch championship with 18 points and sit just ahead of Feyenoord on goal difference.
FC Twente remain top on 25 points, one clear of PSV Eindhoven, following a 1-0 win at RKC Waalwijk courtesy of Serbian Dusan Tadic's strike.
PSV came from behind to beat lowly PEC Zwolle 2-1, with a Joey van den Berg own goal in the 79th minute handing the visitors the win.
Van den Berg had earlier put Zwolle ahead nine minutes into the second half but PSV defender Timothy Derijck equalised with 15 minutes remaining before the own goal handed Dick Advocaat's side the three points.
Third-placed Vitesse Arnhem suffered their first loss of the season when they fell to AZ Alkmaar 2-1 at home. Attacker Johann Berg Gudmundsson netted the winner two minutes from time moving AZ Alkmaar up to 10th on 12 points.