Morgan Amalfitano had fired Rennes ahead against nervy Nice in the seventh minute with a superb chipped effort before Giovanni Sio doubled the hosts' advantage 14 minutes later after narrowly beating the offside trap.
"At halftime, we told ourselves that nothing is impossible," Nice coach Lucien Favre told reporters. "We knew that one goal would be enough to get back on track."
Nice have won only twice in their last eight matches in all competitions and remain third on 53 points, two off second-placed Paris St Germain and five behind leaders Monaco, who thumped Metz 5-0 on Saturday.
"In terms of the table, I'm not worried about other clubs," Favre added. "I only wish for my team to do the best possible."
Elsewhere, St Etienne retained fifth spot after thumping bottom club FC Lorient 4-0 at home, while Nantes jumped five places to 12th as two goals inside the first 20 minutes set them up for a 3-2 home win over sixth-placed Marseille.
(Reporting by Ed Dove, editing by Pritha Sarkar; editing by Martyn Herman)
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