Second-place Nice have 63 points from 29 games, two points behind Monaco, who host Girondins de Bordeaux on Saturday. They hold a one-point advantage over Paris St Germain before the French champions travel to Lorient on Sunday.
Caen went ahead thanks to goals by Ivan Santini and Yann Karamoh, but the hosts responded through Mario Balotelli and Anastasios Donis.
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Santini headed home from Vincent Bessat's cross from the right to put the visitors ahead in the 36th minute. Five minutes into the second half, Karamoh doubled the tally.
Three minutes later, Cyprien was carried off on a stretcher after hurting his knee, adding to Nice's injury woes a few weeks after they lost striker Alassane Plea until the end of the season.
Nice, however, fought back. Balotelli latched onto Dante's headed cross to reduce the arrears in the 71st minute.
Six minutes later, Donis equalised from a cross by Dalbert Henrique that took a slight deflection off Mickael Le Bihan. (Reporting by Julien Pretot, editing by Larry King)
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