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Miroslav Klose completed a swift Podolski move four minutes after the restart to take his goal tally to six in four qualifiers and substitute Mario Gomez added another in the 76th minute slotting home from just inside the area.
Winger Podolski completed their win with a fine solo effort five minutes from time to give Germany four wins in as many games.
Germany lead the standings on 12 points, after group rivals Turkey slumped to a surprise 1-0 defeat against Azerbaijan to remain second on six, level with Austria.
The Germans, who beat Turkey 3-0 on Friday, had little problems adapting to the artificial grass, carving out chance after chance.
Klose missed their first good opportunity after 16 minutes when he beat his marker in the area but headed a Thomas Mueller cross over the bar.
Midfielder Mesut Ozil, who was in the starting lineup after recovering from a minor knee injury, failed twice to beat keeper Andrei Sidelnikov from close range. Khedira then headed on to the crossbar on the stroke of halftime as the first German goal looked inevitable with the Kazakhs slowly running out of steam.
The visitors needed only three minutes in the second half to take the lead after a lightning-quick combination between Ozil, Podolski and Klose, with the striker slotting home from three metres for his 58th international goal in 105 appearances.
Klose, who now needs only 10 goals to joins Gerd Mueller as his country's top scorer, limped off shortly afterwards, making way for Gomez, who was set up by Podolski for Germany's second goal.
The Cologne captain then turned scorer, storming past six Kazakhs to complete Germany's victory in the 85th minute.
