The Gunners went 1-0 up after a 49th-minute own goal from Bayern defender Louis Poznanski on Wednesday.
But an 88th-minute winner from 20-year-old substitute Nketiah handed Unai Emery’s side the win in Los Angeles.
“Our responsibility in this club – for the history, present and future – is to give young players a chance,” Emery said.
“If they deserve minutes, they’ll get minutes. I’m very happy with them.”
Arsenal’s victory followed on from Tuesday’s 3-0 friendly win over Colorado Rapids.
They face two more matches in the United States, against Fiorentina in Charlotte on Saturday and then Real Madrid in Landover late on Tuesday.