Bundesliga top scorer Lewandowski, who took his tally to 19 goals, grabbed his first goal of the day when he headed in a smooth Nuri Sahin free kick in the 41st minute to level.
He drilled in his second in first-half stoppage time with a low drive from inside the box before also setting up Dortmund's fifth goal in the 78th with a fine run down the left and a well-timed pass in front of goal for Leonardo Bittencourt.
The previous Dortmund record stretched back to the 1964/65 season when the late Friedhelm 'Timo' Konietzka scored in seven consecutive Bundesliga games.
Lewandowski is among the most sought-after strikers in Europe and German media have long speculated that he will move south to Bayern Munich after refusing to sign a contract extension. His current deal runs out in 2014.
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