Frank De Boer's men edged out a spirited Den Haag side to claim a victory that means they will win the Dutch title with a draw at struggling Heracles in two weeks' time.
Midfielder Christian Poulsen put Ajax ahead after 35 minutes, only for Den Haag to level almost immediately when Stefano Denswil put through his own net.
But Ajax were not to be denied and goals from Davy Klaasen and Thulani Serero made sure of the points, despite an injury-time strike from Den Haag defender Tom Beugelsdijk.
That win keeps Ajax six points clear of Feyenoord with two matches to play.
Feyenoord ensured that the leaders will need a result from their penultimate league fixture by winning 2-0 at PSV in a game that was marred by a serious knee injury to defender Jetro Willems.
PSV's Willems was taken off in the first half and the injury could sideline him from the 2014 FIFA World Cup.
Joris Mathijsen and Daryl Janmaat were on target for the Rotterdam club as Ronald Koeman's men won in the league at PSV for the first time since 2004.
Feyenoord restored their four-point lead over the third-placed Twente as a result of their win.
Meanwhile, NEC and RKC Waalwijk appear poised for the relegation play-offs after they were held to 1-1 draws by AZ and Zwolle respectively.
A late equaliser from defender Kevin Conboy earned NEC a point at AZ, who had earlier taken the lead through Nemanja Gudelj's penalty, but they remain five points adrift of definite safety and just three ahead of bottom club Roda JC.
RKC are a further two points ahead in the other relegation play-off spot after Daniel De Ridder's opener was cancelled out by Zwolle's Mateusz Klich.
Elsewhere, Heracles are still not sure of their top-flight status for next season following a 2-1 loss at Utrecht that saw them finish with 10 men after Bart Schenkeveld was sent off.
