France forward Gignac netted from the spot four minutes into the second half of a rather dull encounter at the Stade Velodrome to put Marseille on 47 points from 23 games, one adrift of Olympique Lyonnais who travel to fifth-placed Monaco on Sunday.
Paris St Germain, who beat Stade Rennais 1-0 at home on Friday, are third, trailing Marseille only on goal difference.
"When you get there at this stage of the season with that number of points, how can you not hope to become champions?" said OM coach Marcelo Bielsa.
"What we've done so far allows us to keep hoping."
Both sides were lacklustre early on and Marseille, although dominating possession, failed to really threaten the visitors' defence.
Six minutes from the interval, Dimitri Payet's volley shaved Benjamin Leroy's bar as OM increased the pressure.
Payet was pushed down in the box by Cedric Barbosa and Gignac converted the resulting penalty to put the home side ahead on 49 minutes.
Alaixys Romao wasted another chance for the home side when he skied a close-range effort over the bar in the 77th minute.
The result left Evian in 17th place with 23 points.
(Reporting by Julien Pretot, editing by Pritha Sarkar and Ian Chadband)
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