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.
"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."
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.
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.
"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.
