Pierre-Emerick Aubameyang became only the sixth player to score a hat-trick on his Bundesliga debut as Borussia Dortmund opened their campaign with a 4-0 victory at Augsburg.
Bayer Leverkusen, Hannover and Hertha Berlin also recorded wins.
Gabon international Aubameyang, signed from French side Saint-Etienne, formed an impressive strike partnership with Lewandowski - to the delight of manager Jurgen Klopp.
"Aubameyang was put to great use today," said Klopp, who led his side to runners-up spot and the Champions League final last season. "I'm not surprised about what he offers, but that all the balls go in already. It's a very good start."
Other results: Hoffenheim 2-2 Nuremberg, Bayer Leverkusen 3-1 Freiburg, Hannover 2-0 Wolfsburg 0, Hertha Berlin 6-1 Eintracht Frankfurt.
