The draw extended Montpellier's advantage to six points over second-placed Paris Saint-Germain who play their game in hand on Wednesday at home to Saint-Etienne.
Younes Belhanda put the hosts, who have three matches left this season, in front with a first-half penalty only for Thomas Kahlenberg to equalise for Evian after 44 minutes.
Kevin Berigaud added a close-range effort for Evian midway through the second half but Olivier Giroud levelled with his 21st league goal of the season six minutes from time.
Morocco midfielder Belhanda, one of Montpellier's players of the season, could be banned for several matches for punching Cedric Mongongu as both players were sent off following a mass injury-time brawl.
Second-half substitute Camara was about to take his penalty when the fighting started and had to wait for more than five minutes before having his shot parried by keeper Stephan Andersen.
"We shot ourselves in the foot because it took too much time to take the penalty," Giroud told the Canal Plus TV channel.
Evian's Saber Khelifa, who had already left the pitch, was also red-carded in stoppage time.
PLENTY OF POSSESSION
Montpellier enjoyed plenty of possession and had the first clear chance when Giroud's volley on the turn was palmed away by Andersen in the 10th minute.
The Danish keeper was again made to work two minutes later, stretching to his left to tip away Marco Estrada's fierce low shot.
Andersen then conceded the game's first penalty when he felled Giroud while trying to punch a cross, the France striker appearing to briefly lose consciousness before getting back to his feet.
Belhanda converted the spot-kick before Kahlenberg levelled by volleying in a Khelifa header.
Montpellier lacked energy in the second half and Camara came on for Karim Ait Fana on the hour but it was Evian who took the lead when Berigaud latched on to a Cedric Barbosa cross from the left on 69 minutes.
Camara then looked offside when he set up Giroud's goal in the 84th minute.
Elsewhere, Bastia were promoted after clinching the Ligue 2 title with a 3-0 win over Metz.
They have a 10-point lead over second-placed Stade Reims with three games left.
Bastia's promotion came almost 20 years to the day after 18 people died when a stand in the club's Furiani stadium collapsed just before a French Cup semi-final.
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