Leroy Sané, Niklas Süle and Serge Gnabry secured the victory for a side with just two 2014 World Cup winners in the starting lineup in Manuel Neuer and Matthias Ginter.
Germany were soon off the mark with Gnabry sending the speedy Sane through and the Manchester City winger grabbed his first international goal in the eighth minute.
Bayern Munich defender Süle also got his first Germany goal as he was left unmarked to slot home from a corner in the 25th.
The Russians, World Cup hosts this year, were missing several players through injury and rarely ventured forward.
Gnabry turned scorer in the 40th, firing in from a superb Kai Havertz through ball, to cap a strong opening by the hosts.
“The first half was really good because we let the ball roll and had a lot of control of the game,” Löw told reporters.
“Two of our goals were the result of really good combinations, and we had a lot of energy in our game.”
In a subdued second half, the play was constantly interrupted by a dozen substitutions in total.
Löw fielded a young starting 11, which included only two players over 25, and left the experienced Mats Hummels and Thomas Müller on the bench. Fellow World Cup winner Jérôme Boateng was not called up, while Toni Kroos was given a break.
The 19-year-old Havertz along with Sané and Timo Werner, both 22, were a constant headache for the Russia defence, with 23-year-old Gnabry also confirming his fine form this season.
“The speed in our attack was important in this game. We did not have that at the World Cup,” Löw said in praise of his younger players, especially Havertz.
“He is very good considering his age. He has this amazing overview of the game and you could see it in training already.” The Germans, who play their last Nations League group match against the Netherlands on Monday, have had a terrible year, crashing out of the World Cup in their earliest exit in 80 years.
They have managed one point in three Nations League matches and face relegation from Group 1 in League A, while they also suffered a total of six defeats in a year for the first time.
They will be relegated if they do not beat the Dutch but could be down on Friday if the Netherlands beat France.