The visitors could have opened the scoring in the first half but Jeremy Menez wasted two good chances with some poor finishing in the 35th and 40th minutes.
PSG showed more accuracy in the second half, but Evian keeper Jesper Hansen saved a lob from Zlatan Ibrahimovic in the 65th and a close-range header from Javier Pastore in the 87th.
"We're fighting to avoid relegation," Evian coach Pascal Dupraz said. "I'd like so much to see my players show the same desire and focus in every game. Unfortunately, that's not the case as you can see in the standings."
Evian was the runner-up in the French Cup last season.
Also Wednesday, it was: Rennes 3, Saint-Etienne 1; Guingamp 0, Bordeaux 1; Ajaccio 1, Bastia 1; Sochaux 0, Reims 2; and Montpellier 0, Lorient 2.
On Tuesday, Lille and Monaco both won to put pressure on PSG, while Nantes beat Valenciennes 2-1. Lille edged Marseille 1-0 and Monaco routed Nice 3-0.
Silvio Romero scored his first league goal by finishing off a counterattack with a header in the 33rd minute. Romain Alessandrini doubled the lead for mid-table Rennes by converting a rebound in the 55th before setting up Romero in the 68th for a 3-0 lead.
Saint-Etienne striker Mevlut Erding scored a consolation goal in stoppage time.
Julien Faubert scored the winner for Bordeaux with a powerful strike through the goalkeeper's legs in the 26th to help his team get back in the race for a European spot. Bordeaux trails fourth-place Marseille by three points.
Bordeaux was down to 10 men in the 53rd minute when left back Lucas Orban picked up a second yellow card. Guingamp forward Claudio Beauvue was also sent off for a foul on Landry N'Guemo in the 90th.
Bastia goalkeeper Mickael Landreau played his 603rd league game at Ajaccio to break the record for most appearances held by former Monaco keeper Jean-Luc Ettori.
Florian Raspentino put Bastia ahead with a low strike in the ninth minute. Ajaccio lost fullback Joshua Nadeau, who was shown a red card for a high kick on Adama Ba in the 61st, but managed to salvage a draw with a chip from Brazilian striker Eduardo in the 82nd.
Christopher Glombard capitalized on a missed clearance from Sochaux goalkeeper Simon Pouplin to give Reims the lead in the 16th before Prince Oniangue headed in a rebound in the 87th.
Lorient earned a third straight win to climb to 12th after Maxime Barthelme outpaced the Montpellier defense to beat goalkeeper Geoffrey Jourdren in the 49th.
Montpellier lost center back Vitorino Hilton, who reacted to a foul from Lorient substitute Fabien Robert in the 88th by kicking his opponent in the face, and was down to nine men in the 92nd when defender Abdelhamid El Kaoutari gave away a penalty that Vincent Aboubakar converted to notch his ninth league goal.
Montpellier coach Jean Fernandez's job is under threat as the 2012 champion is in 17th place.
"When things don't go well, it's always tough for the coach," Fernandez said. "But I accept that. The team and the club are more important. My job is to keep everybody motivated to get out of that situation."
On Thursday, Lyon hosts Toulouse.