Stuttgart are comfortably through to the Europa League group stage after a 1-1 draw in Russia gave them a 3-1 aggregate win.
Dynamo put the visitors under some strong early pressure, but a combination of wayward finishing and solid defending kept them at bay.
Stuttgart started the stronger in the second half and they eventually broke the deadlock through Vedad Ibisevic in the 64th minute.
Dynamo pressed forward and managed to level on the night on 77 minutes, Aleksander Kokorin converting from Pavel Nekhaychik's assist.
Zvjezdan Misimovic had a late chance blocked, but the home side did not do enough and Stuttgart went through 3-1 on aggregate.
