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.
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.
"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.
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.
Camara then looked offside when he set up Giroud's goal in the 84th minute.
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.
