Schalke beat fourth division Ulm to clinch just their second win of the year while fellow Bundesliga clubs Borussia Dortmund, RB Leipzig, Borussia Moenchengladbach and Cologne advanced in the German Cup.
Hoffenheim and Union Berlin were the biggest casualties in Tuesday’s action.
Schalke’s 3-1 defeat of Ulm was some consolation in the midst of a winless streak in the Bundesliga that now stands at 29 matches.
Their other triumph in 2020 was also in the Cup, against fourth division Schweinfurt in the first round.
Top-flight side Hoffenheim were surprisingly beaten on penalties by second tier Greuther Fuerth after a 2-2 draw.
Mats Hummels and Jadon Sancho led Dortmund’s 2-0 triumph against Braunschweig while Gladbach routed fourth division Elversberg 5-0.
Suat Serdar opened the scoring for Schalke after Bastian Oczipka beautifully played the ball across the box and Benito Raman scored twice.
Johannes Reichert from the spot scored for Ulm.
“We reached the next round and that’s the most important,” coach Huub Stevens told TV broadcaster Sky.
The veteran manager is an interim solution after Manuel Baum’s dismissal and his permanent replacement should be announced later on Tuesday.
“It’s important to finally achieve another victory,” Stevens said.
Dortmund were not brilliant but didn’t have much trouble to clinch their second win under interim coach Edin Terzic, who replaced Lucien Favre.
Hummels scored on 12 minutes and only on stoppage time the top flight side could relax after Sancho’s effort.
Andrej Kramaric struck to give Hoffenheim the lead only for goals from Sebastian Ernst and Marco Meyerhoefer to turn things around for Fuerth before Kevin Akpoguma levelled things up.
In stoppage time Paul Seguin could clinch the victory for Fuerth from the spot but his penalty kick was saved by keeper Oliver Baumann.
The score didn’t change during extra time and the winner was decided once Fuerth sealed the deal with a 7-6 triumph on penalties.
Leipzig visited Bundesliga opponents Augsburg and won 3-0 thanks to a Willi Orban header in the first half and late efforts by Yussuf Poulsen and Angelino.
“We’re very happy to move on to the next round,” coach Julian Nagelsmann said.
“It’s a good way to finish the year.”
Cologne advanced with a tight 1-0 home win over second division Osnabrueck.
Two second division sides progressed with Paderborn edging top-flight Union Berlin 3-2 while Darmstadt prevailed over third-tier Dynamo Dresden 3-0.