The win gave Ajax, who last won the European Cup in 1995 after lifting it three times in a row from 1971-73, four points from three games, level with Olympique Lyon ahead of the reverse fixture against Dinamo in the Amsterdam Arena on November 2.
Real Madrid lead the way with nine points after thrashing Olympique Lyon 4-0 while the Croatians are bottom on zero.
"We missed a lot of chances, at least six which should have been goals, but overall I am happy with the performance and we played exactly as we had anticipated in our pre-match buildup," Ajax coach Frank de Boer told a news conference.
"Theo Janssen and Miralem Sulejmani had a particularly good game, the whole midfield was outstanding and we made it very difficult for Dinamo with our neat passing."
Seeking their first Champions League win since 1999, Dinamo fielded an attacking formation but Ajax always looked the more likely winners and Derk Boerrigter's opening goal was no more than they deserved at the Maksimir stadium.
Ajax squandered a hatful of chances in a lively first half as both sides threw caution to the wind but Dinamo missed the first good opportunity when Jerko Leko's effort was well saved by Kenneth Vermeer.
Kelava again came to Dinamo's rescue by denying Eriksen and Boerrigter while the wasteful de Jong headed wide from close range after a good cross from the left.
De Jong then hit the post and Domagoj Vida almost scored an own goal before Eriksen sealed Ajax's win, prompting the home fans to treat Dinamo's players to a chorus of jeers on the final whistle.
"We created several opportunities and when you don't take them at this level you are always going to get punished by opposition of such quality," said Dinamo coach Krunoslav Jurcic.
Asked how Dinamo, who have yet to score in the group stage, could improve their finishing, Jurcic said: "By allocating 20 million euros or so to buy a top quality striker but that's beyond our means at the moment.
