Dortmund's Turkey international Nuri Sahin threaded a beautiful left-foot free-kick over the wall into the top corner to set the home side on their way in the ninth minute.
Japanese Shinji Kagawa saw his shot deflected by team-mate Robert Lewandowski in the 70th minute to double their lead after Bremen stepped up the pressure in search of an equaliser.
The win lifted Dortmund, who have only conceded nine goals so far, to 43 points and another victory in their last match before the winter break next week would see them break the Bundesliga points record at the half-way mark.
Bayern Munich hold the record with 44 points from the 2005/6 season.
"We started really well but then allowed Bremen back into the game," said Dortmund coach Jurgen Klopp. "We lost our calm at times in the second half but in the end we deserved to win."
Bayer Leverkusen crushed hosts Hamburg SV 4-2 to move into second place while Bayern Munich recovered their domestic form with a 3-0 victory over St Pauli to move up to fifth.
OWN GOAL
Leverkusen's former Hamburg striker Sidney Sam struck on the half-hour but Arturo Vidal's own goal gave the hosts some hope before the Chilean made amends in the 61st minute.
Renato Augusto added two more to pile on the misery for Hamburg, who pulled a goal back in the 79th through Eljero Elia, and lift Leverkusen to second place with 32 points.
Bayern took the lead through a thundering drive from Hamit Altintop against the run of play and needed a penalty plus a red card, awarded for goalkeeper Thomas Kessler's foul on Thomas Muller, to make things safe.
Philipp Lahm converted from the spot before Franck Ribery completed a victory that lifted the Munich side to 26 points.
Their Germany midfielder Bastian Schweinsteiger gave the 69,000 Bayern fans more joy by announcing over the stadium microphone that he had extended his contract to 2016.
"I am a coach who has long-term targets and Bastian Schweinsteiger's signature is important," said Bayern coach Louis van Gaal. "It is a very good sign that a world class player stays at Bayern."
Hoffenheim conceded an 87th minute equaliser as they were held to a 1-1 draw at home to Nuremberg to remain sixth on 24 points, while Steve McClaren's VfL Wolfsburg drew their fifth straight game, a 0-0 stalemate at Kaiserslautern, to stay 13th.
Surprise package Hanover are third after moving to 31 points with a 2-1 win over visitors VfB Stuttgart on Friday.
