Philippe Coutinho and Ivan Perisic also scored their first goals for the German giants in the festival match to mark the opening of the Klaus Augenthaler Stadium, named after the Bayern legend and World Cup winner.
Singh has impressed since joining in June, playing in pre-season friendlies against Arsenal, Real Madrid and AC Milan.
The 20-year-old also produced a brilliant assist on the weekend for Bayern Munich's reserve side.
The friendly match saw 61-year-old Augenthaler play for both teams.
Augenthaler started his career as a junior at FC Vilshofen before moving to Bayern where he played for 15 years.
