The visitors grabbed the lead when Stuttgart defender Arthur Boka's pass found Bastian Schweinsteiger outside the box and he unleashed a ferocious drive past helpless Stuttgart keeper Jens Lehmann.
Two minutes later French playmaker Franck Ribery combined well with Ze Roberto and Luca Toni before the Italian found Ribery for an easy tap-in.
Bayern, cracking a fragile Stuttgart defence at will, could have added a third but Ribery's weak penalty, awarded for a handball, fell into Lehmann's arms.
Stuttgart's Mario Gomez scored a late consolation goal.
"The boys quickly understood Stuttgart were waiting for their chance and not coming forward so we could attack and score," Bayern coach Juergen Klinsmann told reporters.
"The way we lost was unacceptable," the former Bayern player said. "I can accept defeat but not like this. We were too scared. I have to admit though Bayern were outstanding tonight."
Olic broke the deadlock a minute before halftime after 1860 Munich keeper Philipp Tschauner's poor pass was intercepted by Piotr Trochowski. Olic added two more before Munich pulled one back with Daniel Bierofka in the 86th minute.
Jena pulled one back through Andre Schembri before Rakitic and Kevin Kuranyi sealed Schalke's win.
Mainz beat Freiburg 3-1 in the day's other match.
