Valencia defender Mustafi powered home the opener from Toni Kroos’s free-kick after just 19 minutes of Sunday’s game.
And Schweinsteiger wrapped up the win in injury time, moments after coming off the bench.
However, Germany were also thankful to captain for the night Neuer as he made stops from Yevhen Konoplyanka and Yevhen Khacheridi, while Jerome Boateng made a spectacular clearance off his own line.
#Mustafi with a bullet header for #GER! 1-0! #EURO2016 https://t.co/CNHOpw5acH
— Sport360° (@Sport360) June 12, 2016
What an incredible save from #Boateng to keep #GER ahead at the break #GERUKR pic.twitter.com/CSsfVKmYwu
— Sport360° (@Sport360) June 12, 2016