Having enjoyed 20 victories and five draws in their last 25 league matches, Borussia have now beaten Bayer Leverkusen's record of 24 matches without defeat set in the 2009/10 season.
Dortmund are still 11 short of Hamburg's all-time record of 36 matches without defeat set over two seasons in 1981/82 and 1982/83.
With three matches left this season, Dortmund are virtually assured the German league title as they enjoy an eight-point lead over second-placed Bayern Munich with the season to end on May 5.
Bayern host Real Madrid in the Champions League semi-final, first-leg, on
Tuesday and coach Jupp Heynckes paid the price for resting several stars as captain Philipp Lahm, wing Franck Ribery and striker Mario Gomez all started on the bench.
After Borussia beat the Bavarians 1-0 in Dortmund on Wednesday, Jürgen Klopp's side took the opportunity to extend their lead but they had to come from behind in Gelsenkirchen.
"That was real work for all parties with Borussia Dortmund as the lucky winners," said Klopp, who has steadfastly refused to talk about the title.
Dortmund now faces fourth-placed Borussia Mönchengladbach, bottom side Kaiserslautern and Freiburg before the league finishes on May 5, while Bayern face Werder Bremen, Stuttgart and Cologne in their title run-in.
Kaiserslautern have no more than a mathematical chance of avoiding relegation after they were beaten 2-0 at home by Nuremberg, which kept them nine points from safety.
Ten-man Hertha Berlin remain second from bottom despite picking up a point in a dramatic 3-3 draw at Bayer Leverkusen, after they scored three goals in 15 second-half minutes.
Cologne, who are at Mönchengladbach on Sunday, are in the third relegation place, and now four points behind 15th-placed Augsburg, who poached a 2-1 win at Wolfsburg.
Hamburg also gave themselves a fighting chance of staying up with a 1-0 win at home to Hannover.
Stuttgart are fifth in the league and challenging for a Champions League place after their 4-1 hammering of Bremen on Friday night extended their run without defeat to nine games.