Marseille reduced the arrears through Andre Ayew in the 86th minute but never came to terms with the astonishing pace of Belgium winger Dries Mertens.
"The coach told us that they had lost a lot of games lately so we had to put them under pressure early on," Mertens told Canal Plus. "Once we get the ball back, we are fast in front of goal, that's one of our qualities.
"Six points for everyone - too bad Dortmund won - but we now have two matches out of three at home." Napoli play host to Marseille in their next match.
Ayew said: "Once again we're disappointed. We just have to keep our mouths shut and get back to work. Now the most important thing is the league." Marseille have lost their last four games in all competitions.
Elie Baup's side came close early in the first half when Benoit Cheyrou's deflection off Jeremy Morel went just wide but that was about all the home side had to show for themselves.
Mertens, with his delicate turns and speed, proved a permanent threat to the Marseille defence.
In the 34th minute, at the end of a sharp counter-attack, Gonzalo Higuain missed a sitter, shooting wide despite being alone in front of goalkeeper Steve Mandanda.
Eight minutes later, midfielder Callejon opened the scoring following a superb defence-splitting pass from Higuain. The Spaniard chested the ball down and fired a half-volley past Mandanda as Napoli were rewarded for their domination.
Mertens flicked the ball into the path of the second-half substitute Zapata with a cunning back heel and the Colombian striker curled a shot into the top corner from 20 metres to put the visitors 2-0 up.
Striker Andre-Pierre Gignac was nowhere to be seen and was replaced in the 77th minute by Jordan Ayew. But it was the Ghana international's brother Andre who found the back of the net with a 20-metre half-volley to ease Marseille's pain.
One blot on Napoli's night was that seven of their fans were arrested by police for clashing with Marseille supporters. Several were slightly injured, police reported.
(Writing by Julien Pretot; Editing by Mike Collett and Robert Woodward)
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