Alexander Samedov opened the scoring for the visitors from the spot but Qatar hit back with goals from Boualem Khoukhi and Karim Boudiaf.
The game started well for Russia coach Stanislav Cherchesov's experimental lineup.
Samedov struck after five minutes but Qatar wasted a chance to level when Ibrahim Majid failed to convert a penalty in the 29th.
Khoukhi equalised with another penalty six minutes later before Qatar went 2-1 up when Boudiaf headed in a corner.
Alexander Kokorin then missed a spot kick that would have earned Russia a draw.
"We created chances for our opponents. Our discipline was not at the level it should have been," Cherchesov told reporters after his side suffered their second straight defeat, following a 4-3 reverse against Costa Rica last month.
"There are no excuses. I hope we'll be able to sort out these mistakes in the future."
(Reporting by Dmitriy Rogovitskiy; Editing by Tony Jimenez)
