Poland striker Lewandowski whipped a free kick past Roman Buerki six minutes later but Raphael Guerreiro's missile in the 20th gave the visitors hope.
RB Leipzig scored a stoppage-time goal through substitute Yussuf Poulsen to snatch a 1-0 victory over Bayer Leverkusen but ended the game with 10 men after captain Willi Orban was sent off.
- With 26 goals in the Bundesliga to his name this season, Lewandowski is top of the scoring charts, one ahead of Pierre-Emerick Aubameyang.
For this match, Bayern Munich are without Douglas Costa, Thomas Müller, and Manuel Neuer, who are all now out injured.
Carlo Ancelotti has carried on where Pep Guardiola left off, with Bayern dominating in Bundesliga and preparing for a Champions League quarter-final against Real Madrid.
Manmohan hails GST passage
He said, it is a matter of happiness that all political parties extended their support in the passage of the bills. He said, the work on fixing rates has started and GST council will take final decision next month.
"So on Saturday we will give it all we have", said Hummels.
The Bavarians doubled their lead on 10 minutes when Lewandowski launched a free-kick from outside the area, but Dortmund's Ousmane Dembele ducked to allow the ball to fly over the wall and hit the net.
Goalkeeper Neuer underwent toe surgery last Friday, forcing him out of Bayern's previous two games, while Muller also could not play in Bayern's 1-0 loss at third-placed Hoffenheim on Tuesday - the league leaders' second league defeat of the season - after injuring his ankle in the 6-0 win against Augsburg last Saturday.
With Bayern leading 2-0 courtesy of goals from Franck Ribery and Robert Lewandowski, the odds appeared stacked against Dortmund in their quest to take something from this eagerly-anticipated encounter.
But before the heavyweight clash in Munich, second-placed Leipzig reduced the gap at the top to seven points in a dramatic finale against Leverkusen.
We can learn from Chelsea - Liverpool boss Jurgen Klopp
Both Hernandez and Maguire were withdrawn through injury, but Hull are now two points above 18th-placed Swansea City. Klopp's anger is justified, then, as Liverpool's defending for Bournemouth's equaliser was arguably worse.
But despite the numerical disadvantage, Leipzig claimed the three points through their Scandinavian combination. That made things very hard for us. They're one point behind third place Hoffenheim, but a comfortable nine points ahead of fifth place Freiburg.
Schalke 04 scored twice in each half to crush strugglers VfL Wolfsburg 4-1 and climb up to 10th on 37 points.
Cologne lost 3-2 at home to local rivals and fellow European hopefuls Borussia Moenchengladbach.
Captain Lars Stindl scored the victor nine minutes from time for Gladbach after Cologne had twice come from behind to equalise.
Florida Bill would eliminate end-of-year exams for some students
A bill that aims to protect religious expression in Florida's public schools has passed the state's House of Representatives. SB 340 , a similar bill, is scheduled be heard in its final committee, the Senate rules committee, on Thursday.