The youngster headed home in the dying minutes after Thomas Muller and Toni Kroos had earlier put the European champions in control of the friendly encounter
The Bundesliga champions named a strong side that included Franck Ribery, Mario Mandzukic and Thomas Muller, with the German getting the scoring under way against their Serie B opponents.
It was Mandzukic who had the biggest part to play, though, seizing on a poor clearance from Brescia goalkeeper Alessio Cragno to play in Muller, who easily tapped home after 23 minutes.
Bayern doubled their advantage nine minutes later, with Ribery the architect, getting to the byline and squaring for Muller, who in turn set up Toni Kroos to add the finishing touch.
That is how it remained until the 90th minute when Jan Kirchhoff, a recent signing from Mainz, put the game beyond any doubt.
The 22-year-old headed home after a penalty area mix-up to give new boss Pep Guardiola his fourth win from four friendlies.