Bastian Schweinsteiger and Mario Gotze's quickfire goals in the 20th and 22nd minutes unlocked the game for Joachim Low's men before Thomas Muller wrapped up victory for the Germans.
Kazakhstan tried to make a game of it, particularly in the second half, but the third goal knocked the stuffing out of them as they raised the white flag in Astana to remain on one point in qualifying Group C.
The win takes Germany five points clear of Sweden ahead of another game against Kazakhstan in Nuremberg on Tuesday.
It was hardly the walk in the park that Germany had hoped for on the artificial pitch in Astana.
Low's charges appeared to be in perfect control of the game early on, but the final ball was lacking and, apart from a speculative shot from Julian Draxler, who left the field shortly after a clash of heads to be replaced by Lukas Podolski, the Kazakhstan goal was rarely threatened.
Germany finally made the breakthrough in the 21st minute when Schweinsteiger juggled the ball onto his right foot inside the penalty area and his snapshot, which appeared to take a decisive deflection off Muller, flew inside the far post.
Just a minute later, confusion between the Kazakhstan goalkeeper and a defender saw the ball spill out to Gotze, who chipped it in from 10 yards.
Germany failed to build on their two-goal advantage, though, and an enthusiastic crowd did what they could to lift their side's spirits.
It seemed to work with substitute Ulan Konysbaev rattling the crossbar with a fine 20-yard effort in the 69th minute.
Two minutes later, Heinrich Schmidtgal, who plies his trade in the Bundesliga for Greuther Furth, tested Manuel Neuer, who responded with an excellent one-handed save to protect the near side of is goal.
Muller then ended the home team's hopes with Germany's third in the 74th minute.
Another defensive mix-up led to Gotze playing in Mesut Ozil, who teed up Muller to stroke the ball in from eight yards.