Lille finished five points behind their opponents last term but were dominant in the second half at Stade Pierre Mauroy as Marcelo Bielsa's reign got off to the perfect start.
Paraguayan international Junior Alonso got the ball rolling three minutes after half-time, Nicolas de Preville made it 2-0 from the penalty spot in the 67th minute with Anwar El-Ghazi adding the gloss three minutes later.
The result means that Ranieri's Nantes are only kept off the bottom of the table by RC Strasbourg who suffered a bruising 4-0 defeat away to Lyon on Saturday.
Summer signing Baptiste Guillaume struck late on to earn Angers a 2-2 home draw against Bordeaux.
Angers took an 11th-minute lead when Pierrick Capelle's cross found its way to Angelo Fulgini, who finished through the legs of Benoit Costil for his first goal in Ligue 1.
But Bordeaux were ahead after Younousse Sankhare (27) turned in Francois Kamano's cross and Alexandre Mendy (52) scored on debut following his move from Guingamp.
Bordeaux looked as if they would hold on to the points, but two minutes from time Costil palmed out a Karl Toko Ekambi shot and Guillaume could not miss.
Clinton Njie marked his permanent move to Marseille by scoring twice in a 3-0 victory over Dijon in Ligue 1.
Marseille had huffed and puffed during a goalless first half against opponents who were almost relegated last season.
But Njie, introduced at half-time in place of a disappointing Dimitri Payet, provided the penetration Marseille had been missing with former Newcastle forward Florian Thauvin also on target.
