Miroslav Klose scored the only goal of the game in the 34th minute, the visitors weathering early and late storms and riding their luck after Jerome Boateng was sent off on his debut in the 69th minute.
Germany had their backs to the wall, and Boateng was dismissed for a second yellow card for a foul on Vladimir Bystrov.
Russia were unable to take advantage of their extra man, although they were unfortunate not to be given a penalty late on.
The contact Michael Ballack made on Andrey Arshavin was innocuous, and referee Massimo Busacca was right to wave play on. But the Russians will have felt aggrieved when the Swiss official again opted not to point to the spot moments later after Arne Friedrich fouled Bystrov.
Joachim Low's side held on to open up an unassailable four-point lead at the top of Group Four with one game remaining, leaving Guus Hiddink's Russia with the consolation of a place in the play-offs.
Finland made sure of third place with a 2-1 home victory over Wales in Helsinki.
Craig Bellamy's first-half equaliser was his 17th for his country, and he is now Wales' fifth highest all-time scorer.
The hosts led early on through Roni Porokara, and grabbed a late winner from defender Niklas Moisander in a barely half-full stadium in the Finnish capital.
Finally, Azerbaijan moved off the bottom of the table courtesy of their first win of the qualifying campaign - 2-0 over Liechtenstein in Vaduz. Vagif Javadov and Elvin Mammadov were the men on target in the second half.