The Japanese forward struck in the 14th and 53rd minutes at Signal Iduna Park but could do nothing as die Nullfunfer lost 4-2 to BVB.
Okazaki has now scored 13 league goals in 2013/14, which equals Shinji Kagawa's record by a Japanese player in a single German season when he was at Dortmund.
"It's great to score against a top team," Okazaki said. "I want to continue playing like I did today.
"If I can score another goal. I believe I can make my mark in Germany."
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