Graziano Pelle almost snatched a win in injury time but goalkeeper Kenneth Vermeer tipped his powerful header over the bar.
Pelle controlled the ball on his chest and slammed it past Kenneth Vermeer to secure a point for Feyenoord 15 minutes after Ajax defender Niklas Moisander was sent off for his second yellow card on Sunday.
Pelle almost snatched a win in injury time but Vermeer tipped his powerful header over the bar.
Ajax midfielder Christian Eriksen opened the scoring in the 12th minute when he fired in from the left after a pass from Ryan Babel, and 18-year-old newcomer Jean-Paul Boetius equalised six minutes later for Feyenoord.
"It was a great feeling to score," Boetius said. "All in all this was a dream afternoon for me."
Ajax went ahead again when Siem de Jong deflected Eriksen's free-kick into the net early in the second half.
Ajax coach Frank de Boer was disappointed with his side's second straight league draw, after last week's 3-3 deadlock against Heracles Almelo. Between the two draws, Ajax beat Manchester City 3-1 midweek in the Champions League.
"We gave away a lead late in the game as we did against Heracles," De Boer said. "We have only got two points from our last two league matches and that's not enough."
In later games, FC Twente stayed top with a narrow 1-0 win at RKC Waalwijk and PSV Eindhoven remained second after rallying from a goal down to beat lowly PEC Zwolle 2-1.
Dusan Tadic scored the only goal in Twente's victory after a cross from the left by Luc Castaignos had been deflected to him by goalkeeper Jeroen Zoet in the 40th minute.
Zwolle captain Joey van den Berg opened the scoring by heading home a corner to give his side the lead before PSV defender Timothy Derijck equalised and Van den Berg scored an own goal with just over 10 minutes to go to give Eindhoven the win.
In the day's last match, third-placed Vitesse Arnhem was playing AZ Alkmaar.