Marco Reus added a lucky second goal in the 52nd, when he sailed a long free-kick into the box and Marseille ’keeper Steve 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.
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 with their seventh straight home win in the competition since losing to Marseille two years ago.
Marseille, the 1993 European champions, are bottom after losing both games so far, while Arsenal are top on six after beating Napoli 2-0.
“We had to work hard because Marseille are a good team and it would not have worked with just a few kilometers of running,” Klopp told reporters. “Now we are back in the mix and we did it impressively. We struck at just the right times and that is a quality we have. If the team play the way they did today, I’m allowed to relax sitting in the stands. My colleague [Zeljko Buvac] did an outstanding job, but it was not that much fun up there.”
With Klopp exiled to the tribune following an outburst directed at the fourth official during their Napoli defeat and his long-time assistant 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.
However, Dortmund, 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 35m 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.
“Dortmund are a very good team, they made the best choices tonight,” Marseille defender Rod Fanni said. “We had good intentions, but performed below par.”
Dortmund, who were also missing suspended ’keeper Roman Weidenfeller, kept pouring forward and were rewarded with a third goal when Lewandowski calmly converted his spot-kick.