The runaway Ligue 1 leaders, who are chasing a record fifth successive league crown, lifted the Cup for the third and last time in 1973.
Two goals from gifted teenage striker Karim Benzema gave Lyon a 2-0 halftime lead. Mali midfielder Mahamadou Diarra and forward Hatem Ben Arfa completed the rout after the break.
"We made it look easy by taking the match very seriously and playing extremely well," said Lyon coach Gerard Houllier.
Olympique Marseille, Cup winners a record 10 times, qualified in similar fashion, two goals from midfielder Franck Ribery helping them crush second division Le Havre 4-0.
Forward Toifilou Maoulida, playing his first match for Marseille two days after joining on loan from Monaco, opened the scoring after 55 minutes. Nigeria midfielder Wilson Oruma doubled their advantage six minutes later.
Ribery put the issue beyond doubt with a penalty after Maoulida was brought down by Le Havre goalkeeper Oliver Blondel in the 64th minute and then wrapped it up on the counter-attack with 10 minutes remaining.
AUXERRE SURVIVE
Holders Auxerre survived the first round with a 1-0 victory at fourth division amateurs Noisy-le-Sec earlier on Sunday.
A first-half free kick from Denmark midfielder Thomas Kahlenberg was one of the few highlights in a dull game but was enough to take the team from Burgundy into the second round.
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Of the four top-flight clubs in action on Sunday, Monaco were the most impressive, four goals by striker David Gigliotti helping them thrash fifth division Rhone-Vallee 6-0.
Six Ligue 1 clubs bowed out on Saturday, three to teams from lower divisions.
Toulouse lost 2-1 at fourth division amateur side Lyon-La-Duchere, Nice went down 3-0 at second division Brest and Troyes were beaten 3-2 after extra time by fourth division Calais, who were French Cup finalists in 2000.
Racing Strasbourg, Lille and Lens won Saturday's three all-Ligue 1 ties, beating Nancy, St Etienne and Le Mans respectively.