Gaetan Laborde's 34th minute goal proved decisive as Didier Digard's side moved into the top half of the Ligue 1 table.
The hosts may have got the result, though it was Lille who dominated proceedings at the Allianz Riviera.
Paulo Fonseca's men enjoyed more possession, shots and dangerous attacks, though their inability to find the back of the net proved costly.
Lille have slipped to seventh in the table and are now nine-points adrift of Champions League places.
Captain Jose Fonte was particularly frustrated by the amount of missed opportunities, saying (as quoted by Le Petit Lillois): "It's clear to see that if you don't score, you lose the match.
"A mistake can happen and you can lose. We have four clear chances to win and we haven't scored. This is football with mistakes that can happen.
"In the second half, they placed well and defended well so it was more difficult to create play. But when you have chances like that in the first half, you have to kill the game."
He added: "We are positive because we have opportunities so we know we can do it. We stay positive to win and try to come back to the score. But they defended well.
"We pushed but we didn't succeed. It's hard to accept this defeat. There are 18 games left. We have to stay positive, keep working and do better because a match like that with chances like that is not acceptable."
Manager Fonseca was also left frustrated, saying: "It's very difficult to speak after a game like that. It's amazing, how did we not win this game?
"We arrived here with a lot of ambition. We played very well, we dominated, we created, but we also gave a gift. We have done some very good things. It is very difficult to speak after this match.
"Players are sorry, but we have courage, we believe in our game, and we are ambitious. Now we have to recover and think about the next game.
"In the second half, Nice defended well. It was harder to find the space, but then again, we still had two or three chances. We played with great courage. It's not easy to come here and dominate, to create against a team like Nice."
Lille will be looking or a return to winning ways when they take on Clermont on Wednesday.
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