Bayern came into the game off the back of a shock home 2-1 loss to Mainz in midweek.
But Pep Guardiola's men looked every inch the force that has dominated German football in recent years at the Signal Iduna Park, dominating possession and creating the better chances throughout.
Douglas Costa was presented with the clearest opportunity of the match midway through the first half but was denied by Dortmund keeper Roman Burki when put through on goal.
In the second period, Arturo Vidal smacked the Dortmund crossbar via the clasped hand of Burki while Arjen Robben blazed wildly over when the ball broke to him 17-yards-out.
The home side did look dangerous on the counter, creating a smattering of openings in the first period.
However, it's best chance came in the game's closing stages when Adrian Ramos headed Pierre-Emerick Aubameyang's floated cross tamely wide.
"I think we had the better of the chances overall, but the draw is fair," said Bayern captain Philipp Lahm after the match in quotes carried by the AFP news agency.
But Bayern boss, Pep Guardiola seemed less than satisfied with some aspects of his side's performance.
The celebrated Spanish coach marched up to 21-year-old midfielder Joshua Kimmich, who was standing in the center circle, at full time and imparted what appeared to be a series of angry criticisms.
Bayern players looked on concerned but Guardiola concluded the impromptu sermon by giving Kimmich a hug.
The result means Dortmund maintains its unbeaten start to 2016 but ensures Bayern remain five points clear atop the table and strong favorites for a fourth consecutive Bundesliga title.
Ronaldo on fire
Eyebrows were raised at Cristiano Ronaldo's outburst last weekend which suggested that Real Madrid would have a far greater chance of winning La Liga if some of his younger teammates were on his own imperious level.
But the Portuguese striker backed up his strong words Saturday by scoring four second half goals as Real Madrid hammered Celta Vigo 7-1 at the Santiago Bernabeu.
Pepe, Jese Rodriguez and Gareth Bale, returning from injury, grabbed the other Madrid goals while Iago Aspas put away a consolation for Celta.
Ronaldo had been jeered by the notoriously demanding Bernabeu crowd at the beginning of the second half.
But he soon quitened the boo-boys in the stands, pointing to his ear to ask where the jeers had disappeared to as he scored.
Ronaldo's goal flurry also means he has now surpassed Telmo Zarra as La Liga's second all-time highest goalscorer with 252 goals in just 228 games. Only Barcelona's Lionel Messi, with 316 La Liga goals, has scored more.
"Cristiano is capable of scoring four goals and there are very few people capable of doing that, Real Madrid boss Zinedine Zidane later told reporters. "That is why he is unique."
On the subject of the fans singling out Ronaldo for criticism, Zidane added: "It is part of football that the fans whistle now and then."
"They are demanding fans, but at the same time they know their players well and always want more."
"That is good to help us improve and do more. Above all, I am left (happy) with his performance."
Real Madrid remains in third place but has cut the gap behind second place Atletico Madrid to just one point and league leaders Barcelona to nine.
Both Atletico and Barcelona can move four and 12 points clear of Real respectively if each wins its game in hand Sunday.