A Tripy Makonda own goal cancelled out Kamel Chafni's first-half opener but Lyon failed to break the deadlock again on a pitch resembling a Wimbledon tennis court in its second week.
The result left Lyon with 52 points from 27 games, two adrift of PSG who lost 1-0 at 10-man Stade Reims on Saturday.
"We would have liked to take all three points but we were caught cold," striker Bafetimbi Gomis told Lyon's official website.
"But we're going forward and we're getting closer to PSG."
Olympique Marseille reduced the gap on the leaders to five points by reclaiming third spot from Saint-Etienne with a 2-1 win at home to Troyes.
Lyon and Marseille will meet at Gerland next Sunday.
Andre-Pierre Gignac netted the winner for Marseille eight minutes from time when he latched on to a Pape Amodou Sougou cross.
Substitute Sougou had set up the first OM goal a minute earlier, perfectly crossing for Nicolas N'Koulou who was at fault for Troyes's opener.
Bottom side Troyes went gone ahead in the 70th minute after Marcos had dispossessed N'Koulou before firing a powerful cross shot past Steve Mandanda.
Troyes have 20 points and lie seven adrift of safety.
Stade Brest went ahead in the eighth minute when Chafni found the back of the net with a low shot from just outside the box.
The midfielder was replaced by Bruno Grougi on the stroke of halftime after he picked up a thigh injury.
Lisandro came close for Lyon in the 37th minute but Alexis Thebaut parried the Argentine's powerful angled shot.
On a sharp counter-attack, Steed Malbranque released Lisandro on the right flank and the Argentine dribbled past Thebaut before his cross was deflected into his own net by Makonda.
Malbranque had a great chance in the 82nd minute but his attempt was cleared on the goal-line by Florian Lejeune.
Lille, now seventh on 43 points, revived their Europa League hopes when Salomon Kalou earned them a 2-1 home win over Girondins Bordeaux.
Kalou, used as a lone striker at Lille, dribbled past Benoit Tremoulinas and beat Cedric Carrasso from close range in the 72nd minute after Ronny Rodelin's fierce strike in the 59th had cancelled out Jaroslav Plasil's first-half penalty for Bordeaux.
Bordeaux lie 10th on 38 points.
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