Basel, inspired by 18-year-old Xherdan Shaquiri and backed by a raucous crowd, led 1-0 with a beautifully-crafted Alexander Frei goal until Bayern's Thomas Muller went down in a seemingly innocuous tangle with Benjamin Huggel in the 56th minute.
The midfielder played the ball but the referee pointed to the spot amid Basel's disbelief in an incident which may raise questions about the value of the two officials behind the goal, being used on an experimental basis in the competition.
Basel coach Thorsten Fink, a former Bayern Munich player, chose not to criticise the decision. "I didn't have a good view of it but there were two handball incidents where I though we could have had penalties," he told reporters.
"I'm totally disappointed with this result."
On a night when Bayern's hard-tackling Dutch midfielder Mark van Bommel committed only one foul, visiting coach Louis van Gaal preferred to praise his own substitutions which included bringing on Mario Gomez at half-time for Hamit Altintop.
"The changes gave us more power, we put more pressure on them in the second half and we scored the two goals," said the flamboyant Dutchman.
In the 17th minute Basel broke from defence, Marco Streller cleverly shielded the ball and flicked it to Switzerland's record scorer Frei who curled it into the top corner.
"We played really well, we fought and we represented Swiss football very well," said Fink.
