Ronald Koeman's men reduced the gap on leaders PSV Eindhoven to eight points - thanks to goals from striker Wesley Sneijder two minutes before half-time and an Andy van der Meyde double on 75 and 84 minutes.
The win at the FujiFilm-Stadion is Ajax's second consecutive league win since they lost to leaders PSV at the end of March.
Sneijder's second of the season and van der Meyde's 11th and 12th goals moves the Amsterdam club above Feyenoord, as they look to secure another season in the Champions League next term.
Geert den Ouden gave RBC Roosendaal an early lead in their match against RKC Waalwijk when he netted after a quarter of an hour to send RBC on their way to a 2-1 victory.
The home side battled back well after their shaky start to find an equaliser on the stroke of half-time when Rick Hoogendorp scored from the penalty spot but their European ambitions were dealt a further blow when Henk Vos also scored from the spot on 68 minutes.
In the other game played on Sunday, Groningen beat relegation rivals Excelsior to help their cause for survival.
Sander van Gessel scored the all-important winner after 73 minutes as Excelsior's time starts to run out.
For full De Eredivisie match summaries click below:
Groningen 1-0 Excelsior
NAC Breda 0-3 Ajax
RKC Waalwijk 1-2 RBC Roosendaal
Click here for updated Eredivisie table
