Tottenham recruit Niko Kranjcar netted a late winner for Croatia but it was not enough to qualify for the 2010 World Cup.
Ognjen Vukojevic put the Croatians a goal in front in the 10th minute before Kazakhstan hit back just over 15 minutes later through Sergey Khizhnichenko.
But Spurs midfielder Kranjcar saved Croatia's blushes when he headed home from 16 yards in the second minute of stoppage time.
Despite the win, Croatia were unable to finish in the top two of their group after Ukraine disposed of Andorra 6-0.
Croatia can blame two heavy defeats against England for their failure in their qualifying campaign.