Setting a quick pace from the start, Dortmund took a 19th-minute lead when the Polish striker completed a lightning-fast break.
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.
Dortmund, who lost their opening group game 2-1 to Napoli and had coach Juergen Klopp suspended, bounced back to move up to second place on three points. Marseille, the 1993 European champions, are bottom after losing both games so far.
With Klopp exiled to the tribune and his assistant Zeljko Buvac in the dugout, Bundesliga leaders Dortmund set a frantic early pace, boxing in the French.
The pressure paid off in the 19th when Lewandowski, who hopes to sign for Bayern Munich in the January transfer window, tapped in an Erik Durm assist to complete a dazzling break.
Marseille were kept on the back foot and Lewandowski missed a sensational chance three minutes later with Mandanda denying him with a superb save.
Dortmund, however, with 21-year-old Durm making a stellar debut in the competition in place of injured defender Marcel Schmelzer, showed no signs of slowing down.
The French keeper had only himself to blame in the 52nd when he misjudged a 35-metre Reus free kick to bungle the ball over the line after it bounced in the box.
The goal knocked the wind out of Marseille, who retained possession but were toothless in attack.
THE MATCH IN A TWEET