Christophe Galtier's side are now 11 points behind league leaders Paris Saint-Germain as they bid to qualify for the Champions League.
The visitors were facing a second straight defeat when Florent Ogier gave promoted Clermont a 17th-minute lead.
But Nice were rescued by in-form forward Amine Gouiri's late double as the France under-21 international scored in the 77th and 82nd minutes to take his tally of league goals this season to eight.
Nice, bankrolled by British billionaire Jim Ratcliffe's Ineos company, are hoping to reach Europe's premier club competition for the first time since the 1959-60 European Cup.
They lost in the qualifying playoff four years ago.
Despite a one-point deduction earlier this term due to crowd trouble, Nice now have a two-point lead over fourth-placed Lens in the race for the top three.
Oladimeji Balogun is a graduate of the University of Ilorin where he studied Microbiology, he is a w...
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