Second-half strikes from Renato Civelli and Neal Maupay under the closed roof of the Grand Stade Lille Metropole ensured that Lille's poor home record against the visitors continued, leaving the hosts without a home win over Nice since the 2006/07 season.
In a lively opening Lille's Dimitri Payet turned Nolan Roux's first-time cross just wide of David Ospina's right post, before Nice captain Didier Digard saw his 35-yard lob drop just behind Steeve Elana's crossbar.
The hosts wasted a good chance to take the lead just before the break after Civelli gave the ball away allowing Payet a free run on goal, but Ospina came off his line to make a superb stop.
On the hour mark Didier Digard knocked a Eric Bautheac free-kick into the path of Dario Cvitanich but the Argentinean failed to get a telling touch from a promising position, providing Steeve Elana with a straight-forward save.
Payet continued to cause problems for the Nice defence and his powerful shot was pushed away by the impressive Ochoa. Marvin Martin pounced on the rebound but his effort failed to work the Mexican keeper.
Ochoa's efforts paid off when his side took the lead in the 79th minute. Civelli rose above Nolan Roux inside the area to head Bautheac's free-kick beyond Elana into the top corner.
The visitors did not stop there and doubled their lead with a well-worked goal five minutes from time. Valentin Eysseric and Romain Genevois combined before the latter crossed towards Maupay who smashed a right-footed shot beyond Elana to earn Nice a third consecutive league win without reply.
The visitors showed their intent from the start when Erdinc beat Mickael Landreau with an effort from the edge of the area but his shot shaved the post.
Rennes continued to press as Alessandrini went close with a 25-yard free-kick, bringing a fine save out of Landreau, before the same player opened the scoring on 34 minutes.
The in-form Julien Feret beat Julien Palmieri on the right before delivering a dangerous cross which Alessandrini poked home at the far post - his fourth goal in five on the road.
Jean Makoun came close for the visitors before Bastia had their first real chance 10 minutes into the second half, Anthony Modeste bringing a save out of Benoit Costil after a cross by Julien Palmieri.
But Rennes doubled their lead in the 61st minute when Makoun picked out Erdinc in the area and he fired a spectacular volley into the top corner, leaving Landreau with no chance.
Bastia almost reduced the deficit in the dying seconds when Yann M'Vila was penalized for handball in the box. However Modeste lost his footing from the resulting penalty and fired well wide.