Aron Johannsson put the visitors ahead on 17 minutes but two goals in the space of three minutes early in the second half from Mitchell te Vrede and Lex Immers turned the match in Feyenoord's favour.
Ronald Koeman's side's lead lasted just six minutes, though, as Johannsson scored his second from the penalty spot in the 57th minute, but AZ were unable to extend their winning streak to four matches and reclaim top spot from Vitesse, who beat Utrecht on Saturday.
Champions Ajax sit a point behind AZ in third after a comfortable 3-0 win at bottom club NEC.
Siem de Jong opened the scoring in the 26th minute and the advantage was doubled two minutes later by Nicolai Boilesen's first for the club.
De Jong then grabbed his second 18 minutes from time to seal the points for Ajax, who ended their run of three games without a win to leave NEC rooted to the foot of the table.
Meanwhile, PSV extended their winless run to four games with a 2-1 loss at NAC Breda.
Jurgen Locadia's goal on the stroke of half-time sent the visitors into the break ahead, but a double from from Kees Kwakman in the 67th and 80th minutes turned the game around.
PSV's tally of one point from their last four matches represents their worst Eredivisie run since April 2007.
Another side without a win in four games are fifth-placed Twente, who drew 1-1 at PEC Zwolle.
The hosts went in front through Guyon Fernandez four minutes after the break, before Twente hit back through Quincy Promes in the 72nd minute to earn a share of the spoils.
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