Brandt scored in the 43rd minute after he was fouled wide on the left. Marco Reus delivered the resulting free kick, and Brandt ducked under the ball at the near post, allowing it to bounce off his back and past Oliver Baumann in the Hoffenheim goal.
Although Dortmund full-back Marius Wolf thought he had doubled the lead in the 56th minute with a powerful shot, the goal was disallowed after a VAR check for a foul on Hoffenheim's Ihlas Bebou in the build-up.
This victory marked Dortmund's eighth consecutive league win, taking them to 46 points, three ahead of both second-placed Bayern Munich and third-placed Union Berlin, who play each other on Sunday.
Struggling Hoffenheim, who hired Pellegrino Matarazzo as manager earlier in the month after sacking Andre Breitenreiter, are currently in the relegation play-off position, sitting at 16th place on 19 points after suffering their fifth league defeat in a row.