Andre-Pierre Gignac netted a hat-trick, with Lucho Gonzalez adding a brace and Gabriel Heinze and Loic Remy also on target for Didier Deschamps' men, who drew level on six points with Spartak Moscow by securing their fifth win in a row in all competitions.
For Zilina it was a fourth successive Group F defeat and means the best they can hope for is to rein in Spartak Moscow and qualify for the Europa League, but even that is a real long shot after this defeat, which is the heaviest home loss suffered in Champions League history.
The Slovakians began the match with high hopes having run Marseille close in a 1-0 defeat at Stade Velodrome on matchday three, but the visitors set the tone as early as the third minute when Heinze headed over from close range after his compatriot Gonzalez steered a corner to the near post.
The French side were well on top as Mathieu Valbuena and Benoit Cheyrou, twice, missed the target but after 10 minutes they got the goal their early efforts deserved.
Cheyrou took possession on the right and picked out Gignac, and the former Toulouse man made no mistake with a shot into the bottom-left corner of Martin Dubravka's goal.
The France forward doubled his tally in the 21st minute, adding a calm finish from Charles Kabore's pass.
The game was as good as over moments later as Heinze fired a shot home from 12 yards following Cheyrou's corner.
It took until the 29th minute for Zilina to create a decent chance as Tomas Oravec headed over Robert Jez's corner, and seven minutes later they were four goals down.
Cheyrou was the provider again, crossing from the left and picking out Remy who finished with a low shot.
Zilina started the second half in more positive fashion, although they were limited to long-range efforts from Admir Vladavic and Ondrej Sourik which failed to trouble Marseille goalkeeper Steve Mandanda.
However, within six minutes of the restart it was 5-0 as Gonzalez headed home a Valbuena cross from the right and Gignac completed his hat-trick by heading home a ball in from Spanish right-back Cesar Azpilicueta.
Gonzalez's second arrived in the 63rd minute before his corner was fired over the top by Kabore, and Zilina's night was summed up as substitute forward Tomas Majtan hit the crossbar with a right-foot shot.