The Germans rode their luck in Moscow, with the home side wasting several good chances and having several penalty shouts waved away, but clinched the win thanks to Miroslav Klose's first-half strike after good work from Lukas Podolski and Mesut Ozil.
"I was convinced before the game that the squad had the necessary concentration and we took our chance," Low said after the final whistle. "Every player had the will to win we needed. Luck played a part a couple of times but we deserved it."
Germany keeper Rene Adler, who distinguished himself with a string of fine saves, added: "We desperately wanted to book our place in South Africa today and no player doubted that we would achieve it. You could see that in the game. It was the most emotional match of my career."
Russia boss Guus Hiddink bemoaned his side's lack of ruthlessness in front of goal. "It was a familiar story, Germany needs just one chance to score," the Dutchman remarked. "We had three or four great chances and could not convert. Now we must be satisfied with a place in the play-offs."