It was Evian who took the lead in the 25th minute thanks to a wonderful flowing move. Nicolas Benezet's accurate pass into the box was pulled back by Cedric Barbosa at the byline, before Berigaud ran towards the near post to bundle the ball into the back of the net.
However, Bordeaux found a leveller with 21 minutes left to play when Mariano raced down the right and chipped a cross into Henri Saivet. His header was saved by Bertrand Laquait, but Diabate was on hand to apply the finish from the edge of the six-yard box.
The visitors were reduced to 10 men late in the match when Poundje was shown a straight red card for a high tackle to the head of an Evian player.
Evian climb to 12th in the table, while Bordeaux move up to 16th.