The hosts remain on course for a return to the Bundesliga despite being winless in their last three league games, whilst the visitors boosted their own title hopes with a thumping victory on Friday.
Despite appearing to dominate much of the game statistically on Saturday, St Pauli were in fact fortunate to come away from their fixture against Erzgebirge Aue with a point in the end.
Etienne Amenyido netted a stoppage-time equaliser for Timo Schultz's side, but their 17th-placed opponents created the far better opportunities and should have killed the game off in the earlier stages.
However, Kiezkicker remain top of the table after Darmstadt 98 drew 2-2 themselves, with a four-point gap between St Pauli and Heidenheim in the promotion playoff spot remaining.
Saturday's two points dropped on home soil was, in fact, the first they had dropped of any kind at the Millerntor-Stadion all season, after winning their previous eight home games.
Attentions turn to the cup on Tuesday now though, and with their promotion quest in full flow, the hosts could be forgiven for not taking it too seriously, particularly considering the calibre of the opposition anyway.
In fact, that has been the case over recent years at St Pauli, with this already being the furthest they have progressed in the cup since they were defeated by Bayern Munich in the semi-finals of the 2005-06 season.
Meanwhile, the visitors will be looking to progress to the quarter-finals comfortably on Tuesday, after seeing off 3.Liga side Wehen Wiesbaden in round one and 2.Bundesliga side FC Ingolstadt 04 in round two back in October.
With the likes of Bayern and Bayer Leverkusen already knocked out of the competition, Marco Rose's Dortmund will be confident of retaining their trophy should they avoid any upset in midweek and beyond.
Momentum is the key for BVB at this stage of the season, and so there will be little easing off against St Pauli despite finding themselves in the midst of a thrilling Bundesliga title race in the coming weeks.
After returning from the winter break with a nine-point deficit from Bayern at the summit, the Black and Yellows have since cut the gap to six points in the first two matchdays of 2022, with the remarkable 3-2 comeback victory at Eintracht Frankfurt being followed up by an excellent 5-1 win over Freiburg on Friday.
Despite facing a well-drilled opponent, who were occupying fourth position at the time, Dortmund strolled to a comfortable victory thanks to braces from Thomas Meunier and Erling Braut Haaland, and a late goal from Mahmoud Dahoud as well.
Rose will be looking for his side to maintain that momentum at every opportunity between now and the end of the season, beginning on Tuesday, which has been lacking in their title challenge this season and in recent years too.
Defender Christopher Avevor could return to the St Pauli squad for the first time since November 2020 on Tuesday, although he will not be expected to start for some time due to a lack of fitness.
As for the visitors, Meunier looks set to miss the next few weeks after picking up an ankle injury against Freiburg on Friday, with Marius Wolf set to deputise at right full-back.
Seventeen-year-old Youssoufa Moukoko could feature for only the second time since September following his spell on the treatment table.
St Pauli possible starting lineup:
Smarsch; Ohlsson, Ziereis, Medic, Paqarada; Becker, Smith, Hartel; Buchtmann; Matanovic, Burgstaller
Borussia Dortmund possible starting lineup:
Hitz; Wolf, Akanji, Pongracic, Schulz; Brandt, Dahoud, Bellingham; Hazard, Haaland, Malen
We say: St Pauli 1-3 Borussia Dortmund
Dortmund are unlikely to ease off in their pursuit of some consistent form ahead of their defence of the DFB-Pokal trophy and Bundesliga title challenge.
As a result, we are expecting a strong lineup that will comfortably see off St Pauli on Tuesday, with the hosts focusing on their promotion push anyway.
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