It was an extremely open affair in the first 45 minutes with both sets of defenders giving their opponents too much space but Heiko Vogel and Jupp Heynckes must have given strict instructions to their respective players as things certainly tightened up in the second term.
Vogel's Basel, as they did in the group stage finale against Manchester United, continued to press their opposition throughout and got a breakthrough with four minutes of regular time remaining when substitute Jacques Zoua made a neat run before teeing up fellow sub Valentin Stocker who finished through the legs of Manuel Neuer to give his side a famous victory.
There were plenty of presentable opportunities for Bayern earlier in proceedings with Basel keeper Yann Sommer up to the task by making a double save and then diving to his right to deny Franck Ribery before he strong-armed David Alaba's effort from range.
Twice Basel hit the woodwork in the first half through Aleksandar Dragovic whose header was brilliantly knocked onto the post by Bayern gloveman Neuer before Alex Frei was denied by the crossbar with a first-time shot from right in front of goal.
Sommer was at it again with a save to deny Mario Gomez midway through the second half after Neuer had kept out a Marco Streller header early on and the Basel keeper came up with a potentially match-winning stop with just under 20 minutes remaining to again thwart Gomez from an angle before showing bravery to knock the ball away as substitute Thomas Muller pounced.
In the end, however, it was Basel who came up with the killer goal which has edged them ahead for the return leg in Munich on March 13.
UEFA Champions League Round of 16 - first leg
St Jakob Park, Basel - 36,000