Dortmund substitute Jonas Hofmann finally broke Braunschweig's resistance in the 75th minute at the Westfalenstadion before a Marco Reus penalty four minutes from time eased Dortmund further clear.
Braunschweig pulled a late goal back when Kevin Kratz's glancing header deflected in off the head of home striker Robert Lewandowski to give the visitors some hope, but Dortmund held on to move into a five-team share of top spot in the Bundesliga.
In Sunday's only other game, an injury-time free-kick from Hiroshi Kiyotake earned Nurnberg a point in a an entertaining 2-2 draw at home to Hertha Berlin.
Josip Drmic gave Nurnberg the lead five minutes before the interval before Hertha drew level when Sami Allagui's shot took a huge deflection off Berkay Dabanli, before a disputed penalty converted by Ronny put Jos Luhukay's side in front.
Nurnberg responded well and an unstoppable free-kick from Kiyotake earned them a second draw of the season at the death.