Borussia Dortmund advanced to the third round with a 2-0 win away at Eintracht Braunschweig.
Mats Hummels opened the scoring on 12 minutes and Jadon Sancho wrapped up the win for interim boss Edin Terzic's side.
Hoffenheim were left stunned as they bowed out of the DFB Pokal on penalties to Furth.
Regular time ended 2-2 after Andrej Kramaric and Kevin Akpoguma got on the scoresheet for the hosts, while Sebastian Ernst and Marco Meyerhofer netted for the minnows.
The game went to extra-time and then penalties, where the second-division side prevailed 7-6 in the shootout.
RB Leipzig ran out comfortable 3-0 winners over Augsburg in an all-Bundesliga DFB Pokal clash to go to through to the third round.
Willi Orban netted early in the first-half before Yussuf Poulsen and Angelino wrapped up the points late on in the second half.
Schalke claimed a rare win this season as they progressed to the third round of the DFB Pokal with a 3-1 win over Ulm.
Suat Serdar and a Benito Raman brace did the damage for the Bundesliga basement-dwellers, while Ulm scored a consolation goal through Johannes Reichert.
Bundesliga outfit claimed a 1-0 victory over Vfl Osnabruck to make it through to the third round.
Anthony Modeste scored the only goal of the game in the first minute of first-half stoppage time.
In the end, it was a well-deserved win for the Bundesliga side, who had 23 shots to their opponents' five as well as 63 percent possession.'
Bundesliga outfit Union Berlin suffered a shock early exit with a 3-2 defeat to second-division side Paderborn.
Fresh off a 2-1 victory over Dortmund, Union were expected to advance here and scored through Grischa Promel and a Uwe Hunemeir own goal.
However, Sven Michel and Denis Srbeny scored for the minnows to claim a massive scalp.
Borussia Monchengladbach hammered SV Elversberg 5-0 to progress to the third round of the DFB Pokal.
Hannes Wolf, Laszlo Benes, Lars Stindl, Patrick Hermann and a Julio Villalba own goal got the goals for the away side, who were always going to be favourites.
