They had Salomon Kalou to thank for their 12th win of the season after the Ivorian struck twice in five minutes to secure the three points.
Ludovic Genest had opened the scoring for Bastia in the third minute, but by the 22nd minute Lille were ahead thanks to their 28-year-old striker and they held on to stay within touching distance of leaders PSG and Monaco.
Lyon's remain in mid-table after they threw a two-goal lead away in a 2-2 draw with Marseille.
Alexandre Lacazette opened the scoring for Remi Garde's side with his eighth goal of the season, and Bafetimbi Gomis doubled their lead on the verge of half-time.
Marseille's comeback began immediately as Andre-Pierre Gignac halved the deficit in first-half stoppage time, but they had to wait until the 79th minute for Florian Thauvin to earn a point.
In a day of comebacks, Bordeaux were the third side to record a victory after falling behind as they beat Valenciennes 2-1 at home and moved into fourth place in the table.
After a goalless first half, Tongo Doumbia gave the visitors the lead in the 55th minute with a header from a Mathieu Dossevi corner.
However, their lead only lasted three minutes as Bordeaux drew level from the penalty spot. Jussie converted from 12 yards after Landry N'Guemo was fouled in the penalty area by Benjamin Angoua.
Valenciennes missed a chance to retake the lead in the 66th minute when Eloge Enza Yamissi missed a penalty after Carlos Henrique had brought down Jean-Christophe Bahebeck.
The hosts made them pay seven minutes later as Nicolas Maurice-Belay struck his second goal of the season from inside the penalty area to win the game.
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