Feyenoord's Mexican international striker Santiago Gimenez added another goal to complete his hat-trick as the two sides played out the remaining 34 minutes behind closed doors at the Johan Cruyff Arena in Amsterdam.
The clash was halted on Sunday as fans threw flares onto the pitch, and mounted police used tear gas to disperse rioting fans outside the stadium.
Ajax were trailing 3-0 in the second half when the game was initially suspended in the 56th minute before being abandoned.
Gimenez needed only three minutes after play restarted, with Feyenoord in possession 10 minutes from the halfway line, to score and make it 4-0, snapping up a rebound after Igor Paixao had his initial effort blocked.
It was only the second time Feyenoord had scored four goals away against traditional rivals Ajax and took them up to third in the standings.
The defeat adds pressure on new coach Maurice Steijn whose future has been the subject of much speculation. After Sunday’s fiasco Ajax fired their technical director Sven Mislintat, who had appointed Steijn, and the club's top administrator Pier Eringa resigned hours before Wednesday's kick-off.
Ajax, who have had a poor start to the season with just one win, sit 14th in the 18-team league. They finished third last season and failed to qualify for the Champions League for the first time in 13 seasons.
