Two goals in two minutes midway through the first half from midfielders Bastian Schweinsteiger and Mario Gotze, playing in a forward role, quickly put the Germans in control and dashed any faint hopes for the hosts.
Thomas Muller grabbed Germany's third in the 74th minute in a lacklustre second half after the second-bottom home side attempted a brief comeback and even hit the bar.
The result lifted leaders Germany to 13 points from five games, recovering from a 4-4 draw with Sweden in October when they had led 4-0.
"The game was essentially decided in the first half and we took some of the pace off afterwards," Low told ZDF German television. "We wanted to win and that is what is important.
"As for the discussion about the striker, I see this as an option. The offensive midfielder has to be dangerous in front of goal and we want to make our game a bit varied."
Germany are trying to break Spain's stranglehold on major trophies with the Spaniards winning Euro 2012 often playing without a designated striker.
"It is an additional option because when we have Miroslav Klose and [Mario] Gomez fit then we need such players."
Despite a midnight kick-off to accommodate German viewers with a prime-time start back home and an artificial pitch, Germany did not need long to adapt.
Low, whose 4-2-3-1 system had led Germany to two straight semi-finals in the past two major tournaments, opted for no forward in his 91st game in charge even before Thursday's injury to striker Gomez.
The coach had only previously gone without a striker for a brief period in a friendly win over France in February.
Gotze made an instant impact up front, charging past three defenders in a 20-metre solo run only to have his close-range effort smothered by keeper Andrei Sidelnikov.
The hosts only briefly showed some offensive flair and Bundesliga-based Heinrich Schmidtgal fired just wide after a well-executed break.
Their defence could do nothing, however, in the 20th minute when Schweinsteiger, suspended for the next game at home to Kazakhstan on Tuesday, flicked the ball over two defenders and volleyed in for the lead.
Gotze doubled their lead two minutes later, firing into an empty goal after the keeper failed to hold on to a loose ball in the box.
With the Germans taking their foot off the gas, Kazakhstan carved out two consecutive chances with Ulan Konysbayev rattling the bar and keeper Manuel Neuer palming a Schmidtgal effort wide.
Muller restored order by adding the third in the 74th after good work from Gotze and Ozil to keep Germany on track for qualification to the World Cup in Brazil next year.
"Tonight we saw a world-class team in Germany who demonstrated their mastery," Kazakhstan coach Miroslav Beranek told a news conference.
"When you hear grand names like Germany, you are always under pressure and you make mistakes. We paid dearly for our lapses."
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