Substitutes Jonas Hofmann and Marco Reus ensured Jurgen Klopp's men gained three points against a resilient Braunschweig side, in a game which also saw new BVB signing Henrikh Mkhitaryan make his top-flight debut.
Hofmann, who came on for Pierre-Emerick Aubameyang, was the first to strike after 75 minutes before Jakub Blaszczykowski's replacement, Marco Reus, added another from the penalty spot.
Kevin Kratz grabbed a late consolation for the visitors, who are still seeking their first victory in their Bundesliga return.
Sunday's other game saw a four-goal thriller at the Grundig-Stadion, as Nurnberg and Hertha Berlin drew 2-2.
After their 6-1 win against Eintracht Frankfurt a week ago, Hertha found themselves a goal down at half-time thanks to a Josip Drmic effort shortly before half-time.
However, it looked as though the newly promoted side may pick up consecutive wins when Sami Allagui and Ronny put them 2-1 ahead.
It was not to be though, as Hiroshi Kiyotake struck a minute from time to claim a second consecutive draw for his side.
Nurnberg now sit in 11th place after two games, while Jos Luhukay's side are sixth.