Ronald Koeman`s Ajax trailed for long periods in the game, thanks to an early goal from Youssouf Hersi, but fought back bravely.
Jari Litmanen has netted some vital goals of late and he drew Ajax level on 65 minutes.
The comeback was complete when Maxwell netted 11 minutes from time.
Ajax still trail PSV Eindhoven by six points with three games left to play.
Feyenoord also kept their slim title hopes alive with a dramatic win over RKC Waalwijk.
Patrick van Diemen gave RKC an early lead, but Bonaventure Kalou equalised before the break.
It seemed as if RKC would thwart Feyenoord, but Pierre van Hooijdonk stepped up and executed a trademark free-kick with ten minutes remaining to secure the win at De Kuip.
Matthew Amoah scored the goal which could save Vitesse Arnhem from the play-offs, as his first-half effort secured a vital 1-0 win at De Graafschap.
De Graafschap`s failure to win means they are just one game from relegation.
