The Rotterdam team had already beaten FC Twente (6-2), Go Ahead Eagles (3-2), and FC Groningen (4-1) in the last three weeks before visiting a dwindling AZ, which hadn't won the last four Eredivisie games.
A rather uneventful first half saw AZ get in trouble more than once due to sloppy defending and eventually concede the first goal due to clumsiness in the back-line - Zico Buurmeester failed to control a pass well and lost the ball, after which the midfielder headed the ball over goalkeeper Jeroen Zoet and into his own net.
Unable to make an impression whatsoever, AZ brought on Kees Smit and the recovered Ruben van Bommel, son of former Barcelona and Bayern midfielder Marc van Bommel, just ten minutes after half-time.
Feyenoord seemed to double the lead twice in the second half, but goals from Anis Hadj Moussa and Julian Carranza were ruled out for an offside infringement and a foul.
With Timon Wellenreuther excelling with five saves, the most important of which came during injury time on a surprising effort from Jayden Addai, Feyenoord worked its way to a fourth consecutive Eredivisie win.
Feyenoord became just the second team in the last 16 seasons to win without recording a shot on target throughout the match. The Rotterdam team are now just two points behind PSV, although the second-placed reigning champions will play FC Groningen later on Saturday night.
Meanwhile, AZ will look to improve on very short notice with the cup final coming up in just two weeks. The team from Alkmaar have won just one of their last seven games in all competitions and have seemingly officially given up on the fight for the third spot.