Pierre-Emerick Aubameyang opened the scoring in the 25th minute but, with less than a week to go until Dortmund's first Bundesliga fixture against Borussia Monchengladbach, Thomas Tuchel's side resisted the urge to overexert themselves in search of more goals.
That said, the visitors were in control for the most part and rarely looked in danger of surrendering their slender advantage.
Marco Reus and Ilkay Gundogan both came close to doubling Dortmund's lead either side of the break, while third-tier Chemnitzer briefly threatened an equaliser late on.
But Henrikh Mkhitaryan produced a neat finish in the 82nd minute to make absolutely sure of Dortmund's progression.
Roman Burki and Gonzalo Castro both made their first domestic outings in a strong Dortmund starting XI, but Chemnitzer started confidently and created the better early chances.
