The 18-year-old winger, who is currently the subject of a tug-of-war battle between the United States and Germany, drilled home a nice low shot from just inside the area to give Bayern the lead after 35 minutes.
Claudio Pizarro sealed the win in the 53rd minute in a match Bayern dominated.
Pep Guardiola gave 21 members of his first team squad a run-out with back-up goalkeeper Tom Starke the only player to play the entire match.
Exciting talent Green has played underage football for both Germany and the United States but is currently a member of the German set up.
He was called up by the USA's German-born coach Jurgen Klinsmann for America's senior squad for friendlies last November, but Green said he was not ready to decide on his international side yet and stayed with the German U19 team.
Green has a German mother and an American father and was born in Tampa, Florida. He moved to Germany specifically to join Bayern's youth set-up and recently signed a new contract until 2017.
Green, who can also play striker, has scored 15 goals in just 18 appearances for Bayern's second team this season and made his debut for the first team when he came off the bench against CSKA Moscow in the Champions League.