Germany striker Cacau hit a late winner on Sunday to seal VfB Stuttgart's 1-0 victory at home to Nuremberg to leave his side just a point from a European berth.
Cacau, who is set to join the Germany squad for Euro 2012 in Poland and Ukraine this June, struck in the 78th minute when he rolled his shot under Nuremberg goalkeeper Raphael Schaefer from 12 metres out.
Bruno Labbadia-coached Stuttgart have now won four of their last five league games and victory sees them rise to seventh in the table, just one point from a Europa League berth.
Dortmund have 59 points, two ahead of Bayern.
Midfielder Toni Kroos put Bayern ahead at their Allianz Arena with a well-taken chip before Germany striker Mario Gomez, the Bundesliga's top scorer, hit his 23rd goal in 26 matches in the second half.
Hanover, who face Atletico Madrid in the first-leg of their Europa League quarter-final on Thursday, could have rescued a point as ex-Manchester United striker Mame Diouf headed over the bar with time almost up.
Dutch striker Klaas-Jan Huntelaar scored with headers either side of half-time to seal the win to leave him with 22 goals in 25 league goals this season and second in the goal-scoring table only to Gomez.
Borussia Moechengladbach slipped back to fourth when they threw away the lead to lose 2-1 at home to Hoffenheim, which leaves them six points behind Bayern and eight behind Dortmund.
Gladbach were cruising to victory after a goal from Dortmund-bound midfielder Marco Reus seven minutes before half-time, but Hoffenheim took the three points with two goals in as many second-half minutes.
It was Kaiserslautern's 17th league game without a win and means they are now six points adrift at the bottom.
Source: AFP Global Edition