The Bavarians crashed out with a stunning 2-1 second-round defeat after they took the lead but then conceded twice, including a last-gasp goal in second-half stoppage time.
They also saw defender Matthijs de Ligt suffer a knee injury with his participation in the game at Dortmund unlikely, piling more pressure on coach Thomas Tuchel's embattled defence.
Tuchel made several changes to the team that crushed Darmstadt 98 8-0 on Saturday, leaving top scorer Harry Kane on the bench along with Kingsley Coman and Jamal Musiala.
While unbeaten in the league so far, Bayern started their domestic season with a 3-0 loss to RB Leipzig in the German Super Cup back in August.
With their German Cup exit, they now have just two titles up for grabs, the Bundesliga and Champions League.
Despite having won the last 11 league crowns in a row Bayern are not as sharp as in past seasons, conceding goals more easily, and are two points off leaders Bayer Leverkusen.
"It's a very bitter defeat for us but we win together and lose together," Tuchel said after Wednesday's setback.
"Now it's all about digesting this loss.
"We have two days to recover and regenerate ahead of the Dortmund game. We have to see how serious the (De Ligt) injury is. This is not the time to question everything," he said.
Tuchel will need to quickly revive his players for Saturday to keep up their spirits in the title race. They are in second spot two points above fourth-placed Dortmund after nine games.
The coach has urged his players to cut down on mistakes such as the one that led to Saarbrucken's equaliser in the first half, with a poor pass from defender Kim Min-jae.
"It happens far too often and we must fix the decision-making process when under pressure," said Tuchel.
Dortmund, who last season stumbled on the final day to hand the title to Bayern, will be desperate for the three points.
The Ruhr valley club battled past Hoffenheim 1-0 in the German Cup and their second home game in three days is a far more comfortable schedule than Bayern's two away trips.
Dortmund last beat Bayern in the German Super Cup 2019 but their last Bundesliga victory over their rivals came in 2018. Last season they drew 2-2 at home and lost 4-2 in Munich.
"We have things planned against them and we know that we have been waiting a long time for a win (over Bayern)," said Dortmund coach Edin Terzic.
"We came close last year and on Saturday we will give it our all to get that win."
