The hosts were ahead in the 15th minute through Kevin Berigaud but Divock Origi's strike eight minutes later sent the teams in level at half time.
Evian took the lead for a second time in the 64th minute through Cedric Mongongu's penalty as they looked on track for a memorable victory.
But substitute Ryan Mendes rescued a point for Lille with a 93rd-minute leveller to silence the home crowd.
Marseille looked set to move above opponents Saint-Etienne and into fourth but they were too were disappointed by a late goal in a 1-1 draw.
Nicolas N'Koulou had given Marseille the lead with a 64th-minute goal but the visitors were denied by Brandao's effort in the second minute of stoppage time.
The Brazilian rose highest to nod the ball in off the post and keep his side in fourth, three points behind Lille, while Marseille lie in sixth, two points further back.
Elsewhere, Lyon moved up to fifth with a 3-1 home win over bottom club Ajaccio, who are now 10 points adrift of safety.
Gueida Fofana opened the scoring for Lyon two minutes before the break and that advantage was doubled midway through the second half by Jimmy Briand.
Dennis Oliech got the strugglers back into the game with nine minutes to go, but Bafetimbi Gomis's late strike put the result beyond any doubt.
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