Viktor Fischer was the star of the show for the home side as he scored two goals at the Amsterdam ArenA.
The 18-year-old forward made the breakthrough for Ajax as early as the seventh minute from close range and doubled his side's advantage five minutes from the half-time interval.
Fischer could have completed his hat-trick just minutes later, but saw his attempt on goal from close range blocked.
Ajax continued to dominate proceedings in the second half and went 3-0 up just after the hour mark, thanks to a Siem de Jong strike.
However, the hosts went a man down on 65 minutes when Ricardo van Rhijn was dismissed for a second bookable offence and conceded a penalty to Feyenoord.
The result means that Ajax are now level on 40 points with PSV Eindhoven in third, just a point off the pace. Feyenoord are three points behind them in fourth spot in the table.