Second-half goals from Derk Boerrigter and Christian Eriksen gave Ajax their first win in Champions League Group D.
Boerrigter opened the scoring three minutes after the restart, before Eriksen wrapped up the victory in the dying seconds.
Dinamo's Fatos Beciraj had the first chance of the game in the fifth minute but goalkeeper Kenneth Vermeer kept out his well-struck effort.
The visitors countered within a minute when Toby Alderweireld's right-foot effort was parried by goalkeeper Ivan Kelava.
In the ninth minute Vermeer was equal to Jerko Leko's right-foot effort and soon after a lively opening continued when Ajax's Siem De Jong shot wide from 12 yards.
Dinamo's Domagoj Vida was booked in the 12th minute for fouling Boerrigter on the edge of the box but the free-kick came to nothing.
Miralem Sulejmani brought a save out of Kelava in the 23rd minute, then 12 minutes later he fired over after making space for himself.
After Vermeer had showed good handling to catch Jorge Sammir's effort, the best chance of the first half came five minutes before the interval when Kelava got his angles right and tipped Sulejmani's left foot effort around the post for a corner.
Boerrigter broke the deadlock three minutes into the second half, heading home after good work from the impressive Sulejmani.
Ajax's Theo Janssen had a close-range shot saved by Kelava in the 57th minute, before Alderweireld shot wide from 20 yards as the visitors continued to press.
Dinamo threatened midway through the half with a long-range effort from Jerko Leko, which was kept out in unconvincing fashion by Vermeer.
However, the home side were second best on the night and Eriksen's neat 90th-minute finish wrapped up the success.
The result lifts Frank de Boer's side level on points with second-placed Lyon, who were beaten by Real Madrid.
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Lineups
Dinamo Zagreb: Kelava, Ibanez, Simunic, Tonel, Vida, Calello (Tomecak 80), Leko, Sammir, Badelj (Kovacic 46), Beciraj (Pokrivac 69), Rukavina.
Ajax: Vermeer, Van Der Wiel, Alderweireld, Vertonghen, Anita, Enoh, Eriksen (Lodeiro 90), De Jong, Janssen, Sulejmani, Boerrigter (Bulykin 70).
