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."
Champions Bayern Munich suffered a setback in the battle for third place that leads to the Champions League qualifiers after drawing 1-1 at Nuremberg while Hanover reclaimed third spot following their 2-0 win over Mainz 05.
Hanover are on 53 with Bayern, who had Arjen Robben sent off at the end with a straight red card for dissent, a point behind in fourth place.
"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."
DORTMUND DOMINANCE
Dortmund should have had the equaliser much earlier against Hamburg in a one-sided second half.
However teenager Mario Goetze, superb all season, showed signs of nerves in missing from point blank range twice, including once from a few centimetres out, while Lucas Barrios and Lucasz Piszczek rattled the woodwork as they overran Hamburg.
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.
Schalke 04 piled more misery on their former coach Felix Magath, beating his new team VfL Wolfsburg 1-0 thanks to a Jose Jurado goal to leave the 2009 champions in the relegation play-off spot on 28 points.
Schalke, who host holders Inter Milan in the Champions League quarter-final second leg next week after winning 5-2 in Italy, improved to ninth place on 39 points.
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.
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