Ruud van Nistelrooy converted a penalty in the 39th minute after team-mate Mladen Petric was felled by Mats Hummels and Dortmund looked to be heading for their fourth defeat after missing three golden chances and twice hitting the woodwork.
But Blaszczykowski fired in with seconds left in stoppage-time after a good cross from Marcel Schmelzer and a header from Patrick Owomoyela, to keep them on track for their first title since 2002.
"I think it is absolutely fair that we did not leave Hamburg empty-handed," relieved Dortmund coach Jurgen Klopp told reporters. "I can live with this result very well."
"This is a setback for us because we dropped two points here," said Bayern scorer Thomas Muller. "It was a weak performance from us and we paid the price."
The visitors kept at it and after Hamburg's Anis Ben-Hatira was sent off for a second booking they were finally rewarded when the Polish midfielder beautifully completed a quick move.
Freiburg's Julian Schuster scored the goal of the day when he whipped in a corner kick with the ball sailing over keeper Tom Starke before dipping in at the far post as they beat Hoffenheim 3-2 in an entertaining encounter.
