The visitors, who handed Kazakhstan their heaviest ever home defeat when they beat them 6-0 last time the teams met in Almaty in 2006, dominated the game but missed several chances.
Turkey's top scorer in qualifying, Burak Yılmaz, missed the target in the 53rd minute and hit the woodwork 20 minutes later.
But it was Yilmaz who set up Arda Turan to score what proved to be the winner in the 83rd minute in a tough match.
Third-placed Turkey are on eight points after six games ahead of the Netherlands, who have seven from five and were visiting Latvia later on Friday when group leaders Czech Republic, on 13, were away to second-placed Iceland who have 12.
Kazakhstan, who have one point, opened their account with a 0-0 draw at home to Latvia but have lost all five of their subsequent fixtures.
The top two qualify for the finals with the best third-placed finisher in the nine groups. The eight remaining third-placed teams play off to determine the last four qualifiers.
(Reporting by Dmitry Solovyov; Editing by Ken Ferris)
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