Jupp Heynckes' side cruised into the second round of the German Cup without having to step out of first gear against their fellow Bavarians, with their new striker netting twice
Goals from Mario Mandzukic gave his side a one-goal half-time lead to get the ball rolling, and in the second half, Xherdan Shaqiri netted a spectacular free kick, before the Croatian and Claudio Pizarro added late goals to seal the win.
It took a matter of minutes for Jupp Heynckes' side to threaten their opponents' goal as Arjen Robben attempted to slip in Toni Kroos. The Germany international saw the ball taken off his toes, but it broke to Luiz Gustavo, whose driven effort went narrowly wide.
From the resulting corner, Robben chipped in an excellent cross straight to Jerome Boateng, who rose highest, but could only flash a header past Michael Hofmann's right-hand post.
Muller teed up Ribery after yet more good work from Robben, but the defence threw themselves in front of the Frenchman's ferocious strike, before the Dutch winger bent a free kick onto the top of the net.
At the other end, Francky Sembolo broke clear, but sent the ball woefully far away from his team-mate, while Sebastian Nachreiner could not manage to latch on to Christian Rahn's deep free kick.
However, on the half-hour mark, Abdenour Amachaibou managed to send Jonatan Kotzke clear with a through ball, but the midfielder could only send a weak shot straight at Manuel Neuer.
And they were made to pay for their wastefulness. Ribery made some ground down the left in trademark fashion, and pulled the ball across the face of goal to Mandzukic, who notched his second Bayern goal in as many games with a tap-in to secure a half-time lead.
Shortly after the restart, Kroos set up Thomas Muller, but the Germany midfielder could not get enough power behind his shot, leaving Hofmann to make an easy save.
While Bayern had a one-goal advantage, Regensburg continued to look for an in, and although the visitors were in control, gaps in their defence were still apparent.
On one occasion, Jim-Patrick Muller swivelled on the edge of the area, and hooked an effort just wide of Neuer's post.
At the other end, Shaqiri was a whisker away from extending Bayern's lead with a neat back-heel, before Bayern finally put daylight between themselves and their opponents.
On the 60-minute mark, Kroos sent a free kick straight into the wall, but after it was adjudged that a defender had handled his effort, Shaqiri stepped up and curled the ball beautifully into the top corner.
After the second goal, the match was in danger of becoming a rout. Robben and Mandzukic exchanged passes on the edge of the box, and although Hofmann spilt the Dutchman's eventual effort, the ball trickled wide.
With just 10 minutes, Mandzukic struck once more. Shaqiri was at the heart of the move, threading a cunning through ball between the Regensburg centre-backs, and the Croat was there to slot home.
Shaqiri had just enough time to set up a fourth in the closing stages, chipping the ball across the box for Pizarro, who smashed home an emphatic volley to complete the rout.