Frank de Boer's men went into the weekend four points behind their rivals, who face Utrecht on Sunday, but secured their first league victory in three matches to get back on track.
Anwar El Ghazi, fresh from netting his first UEFA Champions League goal in a 3-1 draw against Barcelona on Tuesday, gave Ajax the lead after just 10 minutes, but Fernando Lewis levelled just before the half-hour mark.
The hosts had to wait until 10 minutes into the second half to restore their advantage, when Arkadiusz Milik was on target, and Lasse Schone sealed the points 15 minutes from time.
Vitesse's run of four consecutive wins in all competitions came to an end as they were held to a 2-2 draw at home by NAC Breda.
Marko Vejinovic gave Vitesse the lead, then Erik Falkenburg missed an opportunity to level before half-time when he was unable to convert a penalty.
Adnane Tighadouini did make it 1-1 just after the hour-mark and he struck again four minutes from time to salvage a point after Vejinovic had put the home side back in front just six minutes earlier.
Bottom side Heracles suffered a ninth defeat from their first time 10 league matches as they were comfortably beaten 3-1 at home by Willem II, Samuel Armenteros netting twice for Jurgen Streppel's men.
AZ fought back from two goals down to draw 2-2 at home to Groningen.
Goals from Mikhael Rosheuvel and Nemanja Gudelj thwarted the visitors, who had taken control courtesy of goals from Michael de Leeuw and Danny Hoesen.