ReutersBundesliga 2 side Regensburg managed to keep their guests at bay until the 32nd minute when Mario Mandzukic opened the scoring.
Xherdan Shaqiri doubled the lead with a free-kick just past the hour mark.
Mandzukic got a second with a neatly taken angled shot after rounding the keeper and Claudio Pizarro completed the scoring two minutes from time.
Even though Shaqiri's performance came against second division opposition, there was enough to suggest the son of Kosovan immigrants can fulfil his potential.
"He is a player who is capable of holding the ball and of producing surprises and creativity," Bayern sporting director Matthias Sammer told reporters. "That makes him unpredictable."
Shaqiri, who has already won three Swiss league and two cup titles with FC Basel, came on with Bayern 1-0 ahead and making heavy weather of the first round game.
When he signed for Bayern in February, many wondered how the short and stocky ball-dribbling specialist would force his way into a team already featuring Arjen Robben and Franck Ribery.
Coincidentally, Bayern faced Basel in the Champions League shortly afterwards and the gulf looked enormous as Ribery and Robben combined to take the Swiss champions apart in a 7-0 drubbing, while Shaqiri barely touched the ball.
Switzerland has invested heavily in youth development yet, like many countries, see their best hopefuls disappear once they leave the country.
The most striking example was Johan Vonlanthen, who became the youngest player to ever score in the European championships at the age of 18 in 2004, yet quit the game four months ago after his career failed to take off.
Another is Nassim Ben Khalifa, who helped Switzerland win the world under-17 championship in 2009.
A regular for Grasshoppers at the age of 17, he has now returned to the Zurich-based club after failing to establish himself at VfL Wolfsburg and Nuremburg in Germany.
Bayern coach Jupp Heynckes, who has already nurtured the talent of 20-year-old Austrian prospect David Alaba, promised that Shaqiri's future was safe in his hands.
"I did a lot for the transfer of Xherdan," he said after Monday's win. "Anyone knows my opinion of him knows full well that there is no danger of him disappearing into oblivion.
"He has everything a footballer needs and shows that every day in training."
