Costa Rican Bryan Ruiz produced a fine lob over the Ajax defence after 11 minutes for Theo Janssen to open the scoring but four minutes later Mounir El Hamdaoui equalised for the visitors.
Twente, who meet Tottenham Hotspur in the Champions League on Wednesday, restored their lead after 62 minutes through Janssen's second goal.
Eyong Enoh, though, hauled Ajax level again six minutes later after the home defence failed to clear a corner.
Ajax have 17 points from seven matches, two ahead of PSV Eindhoven and Groningen who shared a 1-1 draw. Twente are fourth with 13 points.
Swede Ola Toivonen put PSV ahead after 63 minutes but two minutes before time Gonzalo Garcia salvaged a point for Groningen.
Roda JC Kerkrade, fifth on 12 points, staged a second-half comeback to draw 2-2 at Heerenveen.
Bas Dost struck twice for Heerenveen before the break.
Dmitri Bulykin also hit two goals to earn sixth-placed ADO Den Haag a 3-2 home win over Heracles Almelo.
