Mathieu Bodmer's goal in first-half stoppage time was enough for the home side to leave the visitors' title aspirations all but over.
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Nice scored the winning goal a minute before the break when Bodmer converted from Christian Bruls's corner.
Salomon Kalou went close for Lille on the hour mark, but his effort went just wide of the post.
The visitors are now 13 points behind Paris Saint-Germain in France's top division.