Yilmaz made a classy shot from outside the penalty box in the 13th minute at Stade Pierre-Mauroy to break the deadlock.
Swiss right-back Jordan Lotomba received a red card for a foul and Nice were down to 10 men in the 48th minute. Celik doubled the gap on minute 56 with a long-range shot to seal the victory.
Lille now lead the standings with 76 points, one point ahead of second-place Paris Saint-Germain.
