Fekir scored both sides of the interval, finishing off good work from team mates Corentin Tolisso and Mathieu Valbuena as Lyonnais played some neat football.
Claudio Beauvue added the fourth goal three minutes from time.
The win put Hubert Fournier's side up to fifth in the standings with seven points a week after a home defeat against Stade Rennes.
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Stade de Reims took the Ligue 1 lead with nine points after a 4-1 win against visiting Lorient.
Caen, who started their season with a promising victory at Olympique Marseille, are eighth on six points after suffering their second defeat in a row.
The home side finished with 10 men after Damien Da Silva was sent off in the 74th minute for a rough tackle on Beauvue, but Lyonnais had already put the result beyond doubt.
Fekir dribbled past Da Silva on the edge of the box before beating Remy Vercoutre with a low, angled shot to put the visitors 1-0 up after 19 minutes.
He doubled his tally in similar fashion one minute before the break with another low shot, from the right edge of the area, after being set up by Tolisso.
Valbuena set him up inside the box for the third goal, after some good work to unsettle the defence, in the 57th minute.
Beauvue rubbed salt into Caen's wounds with a long-range shot that went into Vercoutre's top corner.
Champions Paris St Germain will be looking to continue their perfect start and reclaim top spot on Sunday when they visit Monaco.
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