Marcel Gaus netted the winner for the hosts deep into second-half stoppage time to complete a sensational comeback.
Bayern had taken a first-half lead through Thomas Muller before Saarbrucken levelled in first-half added time.
Bayern coach Thomas Tuchel made several changes to the team that crushed Darmstadt 8-0 on Saturday, leaving top scorer Harry Kane on the bench along with Kingsley Coman while giving 20-year-old Frans Kratzig his first start.
The game had been in doubt due to heavy rain but it was the hosts who troubled Bayern more early in the match before the visitors opened their account with their first chance when Kratzig set up Muller in the 15th minute.
Bayern, who take on title rivals Borussia Dortmund in the Bundesliga on Saturday, also had to take defender Matthias de Ligt off midway through the first half with the Dutch international suffering a knee injury.
It got worse before the break for Bayern as defender Kim Min-jae's pass was intercepted and Patrick Sontheimer tapped in from close range.
The Bavarians struggled with their accuracy and paid the price when Gaus fired in the winner with a left-foot shot in the sixth minute of added time.
