The two have struggled in the top flight recently, with Bremen opting to replace coach Robin Dutt with Viktor Skripnik on Saturday after making a winless start to their top-flight campaign.
Dortmund's 1-0 home defeat to Hannover at the weekend was their fourth consecutive league reversal and sixth in nine matches this term.
However, both enjoyed welcome respite in the Pokal against lower-league opposition.
Bremen saw off third-tier Chemnitzer 2-0 thanks to goals either side of the break from Fin Barthels and Franco Di Santo.
Dortmund boss Jurgen Klopp said his side faced a "critical situation" going into their clash with St Pauli at the Millerntor-Stadion, but he got an ideal response with a relatively routine 3-0 win.
Ciro Immobile, Marco Reus and Shinji Kagawa were all on target for last year's beaten finalists against opposition from the second division.
However, a number of Bundesliga sides did bow out at the second-round stage, including Hertha Berlin, who were beaten on penalties by third-tier outfit Arminia Bielefeld.
Regionalliga side Kickers Offenbach pulled off an upset, with Benjmain Pintol's winner shortly after the hour mark giving them a 1-0 victory over 2. Bundesliga opponents Karlsruhe, while Bundesliga side Hannover were another casualty.
Winners at the weekend against Dortmund, Tayfun Korkut's side were sent crashing out at the hands of Aalen thanks to a Ceyhun Gulselam own goal and Michael Klauss' strike just prior to the hour mark.
Dynamo Dresden - conquerors of Bundesliga giants Schalke in the first round - extended their run in the competition courtesy of a win over higher-ranked Bochum.
Having scored twice against Schalke, Justin Eilers' impressive form in the Pokal continued as he helped Dresden overcome Bochum after extra time.
Philipp Hofmann's brace helped Kaiserslautern topple Greuther Furth, while 10-man Cologne needed penalties to move past Duisburg, having had Slawomir Peszko sent off.
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