Joachim Low's side recorded their third win in qualification for the 2014 World Cup in Astana without truly having to exert themselves
First-half goals from Bastian Schweinsteiger and Mario Gotze within a minute of each other gave the visitors the lead, and Thomas Muller grabbed a third shortly before full-time.
While Kazakhstan looked up for the fight in the opening minutes of the contest, doing their best to harry their opponents, the gulf in class between the two was obvious from the off. An early burst forward from Gotze came to nothing, while Sami Khedira had an effort charged down.
Marcel Schmelzer looked willing to get down the left and almost laid one on a plate for Julian Draxler, who could only tap the ball wide from close range, while Mesut Ozil drove a free kick into the wall when he should have done better.
Andrey Sidelnikov then got himself behind a Draxler pop shot from distance, but the visitors really should have taken the lead when a masterful flick from Schweinsteiger set up Gotze, who contrived to skew a shot high and wide a matter of yards from goal.
In the end, though, the inevitable goal came. Ozil floated in from the left-hand side, drove a pass to Schweinsteiger, who took the ball over his man brilliantly and shot. It appeared to take the slightest deflection off Thomas Muller, but the Germany vice-captain claimed it nonetheless.
Within seconds, it was two. Khedira drove down the byline and pulled it back to Muller, who was promptly crowded out, but forced it back to Gotze, and the Dortmund star applied the finish to get his goal.
For the rest of the first half, it was plain sailing. Draxler was withdrawn due to a head injury and replaced by Lukas Podolski, who combined well with Schmelzer, while Ozil, Schweinsteiger, Gotze and Muller played for possession, rarely surrendering the ball.
After the break, the Germans made a slightly lax start giving the home fans something to cheer about, but, while Kazakhstan's industry down the lines was praiseworthy, they struggled to craft any real chances.
Bauyrzhan Dzholchiyev sent an effort straight into Manuel Neuer's hands, and Sergey Ostapenko's looming presence forced Muller to turn a corner over his own bar, but in truth, the visitors looked more likely to score than concede.
Podolski had three efforts charged down in quick succession on the break, while the Kazakh wall stood firm to block another free kick, this time from Schweinsteiger.
Germany pressed and probed but the hosts were happy to drop back and deprive them of space. And their conservative approach almost paid dividends. Ulan Konysbaev rattled the woodwork with an extraordinary strike, before Neuer made an acrobatic save to deny Heinrich Schmidtgal.
But the two chances seemed to wake up Germany, who charged up the other end and added a third through Muller after some neat build-up play from Ozil and Gotze to secure the victory.
The two sides clash again in Nurnberg on Tuesday.