PSV suffered just their fourth loss of the season at De Kuip, striker Anass Achahbar netting two magnificent strikes in the space of four second-half minutes to put the hosts ahead.
Achahbar opened the scoring in the 59th minute with a hooked volley from Rick Karsdorp's long ball forward and then doubled his tally by lashing home from Jean-Paul Boetius' lofted pass.
Memphis Depay pulled one back in the 68th minute with a low effort from long range, but that proved to be nothing more than a consolation as Feyenoord hung on.
Ajax duly took advantage of PSV's slip-up, although they needed a stroke of fortune to see off relegation-threatened Den Haag.
The hosts had been profligate in front of goal in the first half, and it took an own goal from Xander Houtkoop in the 80th minute to settle the contest.
Davy Klaassen's header deflected off the unfortunate substitute to boost Ajax's faint hopes of a fifth straight league title with six games still to play.
Elsewhere, Mimoun Mahi struck an equaliser 10 minutes from time to earn Groningen a 2-2 draw with Twente, while PEC Zwolle were held 1-1 at home by Excelsior.
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