The game had an edgy start, with several early offsides, and the first chance fell to Renato Civelli for Nice, but he headed over the bar.
In the 14th minute both Anthony Mounier and Jamel Saihi could have broken the deadlock but both players shot wide.
Camara headed wide in the 25th minute as both sides started creating chances, with Younes Belhanda having an effort well blocked before the break.
However it took just eight minutes of the second half for Montpellier to take the lead as Camara buried his second real chance of the match.
Ten minutes later it was 2-0 to the hosts, John Utaka finishing well from Remy Cabella's set up.
Montpellier wanted three, and Gaetan Charbonnier had a great chance with 10 minutes left but could only find the goalkeeper with his shot.
Nice's misery was compounded just a couple of minutes from time when Civelli put through his own net for 3-0.
Dario Cvitanich got a goal back for Nice late on, but the win went to the hosts.