With two games to play at AC Milan and at home against Real Madrid, Marseille are on six points in Group C, two behind Milan and Real who drew 1-1 at San Siro. Zurich are last in the group on three points.
"We must enjoy such a moment. It's a score you don't see very often in a Champions League match even if the game was more difficult than the result could mislead to believe," Marseille coach Didier Deschamps told a news conference.
"The draw between AC Milan and Real Madrid will force us to grab four points from our last two games. We'll give everything in Milan and we'll take stock afterwards," he added.
Marseille, winners in Zurich 1-0 two weeks ago, took control after four minutes when Silvan Aegerter put through his own net following a free-kick delivered from the left by Fabrice Abriel.
Seven minutes later midfielder Abriel left the Swiss defence stranded with another free-kick curved into the net from the same position.
Marseille, who have not kept a clean sheet at home since holding Ligue 1 champions Girondins Bordeaux to a goalless draw on Aug. 30, had a lapse in concentration on the half hour.
Zurich French striker Alexandre Alphonse took advantage and reduced the deficit with a right-footed shot from the edge of the penalty area.
Marseille, however, ran riot during the second half.
Captain Mamadou Niang added the third goal seven minutes after the restart after playing a one-two with Bakari Kone.
Brazilian central defender Hilton headed the fourth 10 minutes from time before Benoit Cheyrou and Brandao added further goals.
"I'm frustrated because the result is not a fair reflection of the reality of the game. Marseille's first two goals should have been disallowed for offside," said Zurich coach Bernard Challandes.
