Bayern took the lead against the run of play with a fine 67th-minute shot from Toni Kroos and seven minutes later Mario Goetze slotted in a deserved equaliser for the visitors from a Marco Reus corner.
Weidenfeller then pulled off several superb stops in the closing stages including a spectacular one-handed effort to push a point-blank Javi Martinez header past the post.
"I really do not know what needs to happen for this boy to play international football," Bayern coach Jupp Heynckes told reporters in reference to the 32-year-old keeper.
The uncapped Weidenfeller has been persistently overlooked by Germany coach Joachim Loew despite showing consistently good form for several seasons.
"We started well and dominated for 20 minutes but then we lost control of the game," Heynckes said. "We were not fully there after the break but towards the end we had our chances and Weidenfeller was superb."
Bayern, who ended a five-game losing streak against Dortmund but have not beaten their rivals since February 2010, have 38 points and are 11 ahead of the champions who remain third.
"We had the odd chance to get more from this game but at the moment we are satisfied with one point," said Weidenfeller. "The championship has not yet been decided."
Bayern defender Holger Badstuber tore cruciate ligaments in his right knee and will be sidelined for several months.
Second-placed Bayer Leverkusen beat Nuremberg 1-0 to claim their sixth win in seven games.
Forward Stefan Kiessling, battling to reclaim a spot in the Germany team, joined four other players on nine goals at the top of the league's scoring chart when he netted in the 37th minute after good work from Andre Schuerrle.
Fourth-placed Schalke, who face Montpellier in the Champions League in midweek, are without a win in four Bundesliga matches after drawing 1-1 at home to Borussia Moenchengladbach thanks to Julian Draxler's 86th-minute equaliser.
Ten-man Mainz left it even later to grab a 2-1 victory over Hannover, Adam Szalai snatching an 89th-minute winner after keeper Christian Wetklo was sent off for handling outside the box.
It was the second triumph in five days for Mainz who are sixth on 23 points.
Shown on television to a Bundesliga record total of 203 countries, the top of the table encounter between Bayern and Dortmund promised lots of excitement.
It turned out to be a slow burner, a lacklustre first half featuring two cautious sides unwilling to allow much space.
"It was intense with both teams giving and demanding everything," said Dortmund coach Juergen Klopp.
"But after such a final phase to the game we are satisfied with the draw. Roman kept the result for us and many Bayern players congratulated him after the game."
With fans staying silent in a protest against new security plans to be voted on later this month, the capacity 71,000 stadium was eerily quiet for the opening 12 minutes.
Apart from an early Thomas Mueller shot for Bayern and a Reus effort for Dortmund saved by Manuel Neuer, there was little in terms of chances.
Dortmund were livelier after the break and Mats Hummels should have opened the scoring after catching the Bayern defence napping but his close-range shot was palmed wide by Neuer.
Bayern went in front when Kroos dribbled past two defenders and gave Weidenfeller no chance with a left-foot shot.
Dortmund immediately went on the offensive and Goetze fired in through a crowded defence after chesting the ball down inside the box.
Mueller twice came agonisingly close late in the game, as did Martinez and Kroos, but Weidenfeller was in spectacular form as he denied Bayern their 13th win in 15 games.
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