World Cup Group C qualifier on Friday.
Bastian Schweinsteiger opened the scoring after 20 minutes and Mario Götze doubled the lead in the 22nd before Thomas Müller finished off the Kazakhs with his score to make it 3-0 in the 74th minute.
The win gives Germany 13 points from five matches in the qualifying group while Kazakhstan have one point.
"It was important to win," said coach Joachim Löw. "The game was decided in the first half. We turned down the tempo in the second half - but we won and that's what counts."
Götze said the Germans had to work for their success. "It was really tough. They played really deep and didn't give us a lot of space," he said.
"It was important for us to score the early goal and then double it up. That gave us some tranquility," he added.
The win in the Kazakh capital Astana gives Germany 13 points from five matches in the qualifying group while Kazakhstan have one point.
"We got the three points. That's about it. The first half we showed our game. We made a couple of mistakes in the second half, but we can tick this one off and head home satisfied," said Müller.
Löw gave Schalke's 19-year-old Julian Draxler his first start as he won his fourth cap. But the youngster's full debut was cut short after just 19 minutes, going off with concussion after knocking heads with Kazakh defender Mark Gurman.
Götze meanwhile lined up as the lone striker in Germany's 4-2-3-1 system with Germany's only nominal striker on the squad, Mario Gomez, out with a strained thigh muscle.
"Of course it was fun being up front," said Götze, who was close to giving Germany the lead after 18 minutes but the Borussia Dortmund star shot over the bar from eight yards out.
Schweinsteiger put the Germans ahead just a minute later when he collected Mesut Özil's pass and had his shot deflected off Müller's chest into the goal.
Germany doubled their advantage in the 22nd minute with Kazakhstan keeper Andrey Sidelnikov trying to clear a ball in the box that went to Götze, who calmly struck into the empty net.
After Germany dominated possession in the first half, Kazakhstan were able to mount a series of counter-attacks and won a number of corner in the first 10 minutes after the break, albeit without any serious test for German keeper Manuel Neuer.
Germany could not produce much up front in the second half and Kazakhstan offered a wake-up call in the 69th minute as substitute Ulan Konysbayev hammered a drive off the crossbar.
Neuer was called upon to make a great save three minutes later, fending away a shot by Genrikh Shmidtgal at the near left post.
Germany answered in the 74th minute with Mueller slotting home Özil's pass into the box to make it 3-0.