Setting a quick pace from the start, Dortmund took a 19th-minute lead when the Polish striker completed a lightning-fast break.
Marco Reus added a lucky second goal in the 52nd when he sailed a long free kick into the box and Marseille keeper Steven Mandanda let it slip through after an awkward bounce.
Lewandowski sealed their win with his 13th goal in 21 Champions League appearances when he converted a spot kick after Reus was brought down in the 79th.
(Reporting by Karolos Grohmann; Editing by Clare Fallon)
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