In front of 50,000 fans this was a game Ajax were expected to win and close the gap at the top of the table.
Derk Boerrigter put Ajax ahead in the 42nd minute and the game was as good as wrapped up when they were awarded their second penalty of the game in the 53rd minute.
With Siem de Jong having earlier missed from the spot, Lasse Schone this time stepped up to clinch a 2-0 win.
More goals were expected but the woodwork would get in the way, a home debut for young Dane Lucas Anderson was a special moment for the youngster and nearly became a spectacular debut only for the post to deny Anderson a debut goal.
The win for Ajax has moved them within three points of PSV who won to take top spot in the league.
Next for Ajax is Willem II away next Sunday.