Sane's opener and his all-action performance made a mockery of Low's decision to exclude him from Germany's World Cup squad earlier in the year, while Niklas Sule and Serge Gnabry also scored on a much-needed night of positivity for Die Mannschaft.
Low said he was happy to see his players create goals from deep positions after Sane and Gnabry benefited from some impressive long passes from midfield before scoring.
"We had a good first period, we controlled the game well," Low told reporters after the match in Leipzig.
"In previous matches we were criticised for not playing from deep. Here we have been able to do it in a few situations.
"We have created a dynamic and built two beautiful goals in this way. In the second period, when we made a lot of changes, we lost some flow, it's normal. Our occupation of the field was not as good."
Low praised Bayer Leverkusen midfielder Kai Havertz, who contributed to a dominant team performance on his full Germany debut and provided an assist for Gnabry to score the third goal.
"He impressed me today," said Low. "He is very secure on the ball and has good positioning going forward."
Russia coach Stanislav Cherchesov admitted his side had been taken by surprise after Germany's fast start to the game.
He said: "In the second half we saw that we could play well. In the first period we were not prepared at the rate imposed by Germany.
"They played more aggressively than us."