Jurgen Klopp's side went into the clash at the Millerntor-Stadion on the back of four successive league defeats, leaving the German giants 15th in the table.
However, they managed to shelve those disappointments for the time being with a comfortable win over a side who occupy the relegation playoff spot in the second tier.
Last season's beaten finalists continued to toil in the final third and should have moved ahead after Immobile had a goal wrongly disallowed for offside. Their persistence soon paid off when Immobile latched on to Kagawa's scuffed effort to tap home the opener on 33 minutes.
It proved a decisive moment as Dortmund doubled their advantage shortly before the break, as Immobile turned provider to cut back for Reus to side-foot past Tschauner.
St Pauli asked better questions of their visitors' defence early in the second half, with Dennis Daube squeezing between a few defenders to fire at goal but Langerak punched clear.
Klopp's men weathered a brief storm of pressure from the hosts before putting the game beyond doubt on 86 minutes, as Kagawa capitalised on a hashed clearance from Tschauner to casually slot home a third.