A win would have moved Marseille above Lyon and into first place, but a patched-up Marseille team threatened little and fell behind to Yoan Gouffran's second-half goal as Bordeaux moved above Marseille and PSG to sit into second place.
"It wasn't a great game, but we were very brave and tenacious," Bordeaux coach Francis Gillot said. "Maybe we should have scored a second goal as Marseille didn't really threaten us."
Lyon is one point ahead of Bordeaux, which is one in front of third-place PSG and fourth-place Marseille, who are separated by goal difference. Marseille and Lyon have played one match less than PSG.
"All of the teams are so close together and things can happen very quickly in football," Bordeaux left back Benoit Tremoulinas said. "Next week, we could find ourselves in fourth or sixth place."
Marseille, which has not won at Bordeaux since 1977, was without injured strikers Loic Remy and Andre-Pierre Gignac and suspended forward Jordan Ayew, so Ghana winger Andre Ayew started in a lone striker's role with Mathieu Valbuena tucked in just behind him.
Valbuena, who scored a superb goal for France in the 2-1 win away to Italy last Wednesday, had a quiet game and went off with 20 minutes left, grimacing and clutching his lower back.
"I felt something and I couldn't sprint," Valbuena said. "There was no point taking any risks."
Marseille had the first chance in the 12th when winger Morgan Amalfitano's strike from 30 yards almost fooled goalkeeper Cedric Carrasso, but he managed to push it away for a corner.
Bordeaux threatened little in the first half and Henri Saivet's tame shot in the 40th was easily saved by `keeper Steve Mandanda. Marseille went straight up the other end and Ayew should have done better from close range when he was set up by Jeremy Morel, but Carrasso raced off his line to dive at his feet.
Marseille looked the better team in the second half but Bordeaux scored against the run of play in the 52nd minute when Tremoulinas crossed from the left and Gouffran got there just ahead of his marker to poke the ball past Mandanda.
"It wasn't easy, they closed us down well and stopped us bringing the ball out," Marseille center back Nicolas N'Koulou said. "We lost our concentration momentarily and we paid the price for it."
Marseille defender Lucas Mendes was shown a straight red card in stoppage time for fouling Ludovic Obraniak as he ran through on goal.
Earlier, an own goal from Reims center half Anthony Weber gave Lyon the lead in the 45th minute, and strikers Bafetimbi Gomis and Lisandro Lopez added a goal each in the second half for the seven-time former champion.
"It was difficult but we were lucky enough to score just before halftime and that opened the match up," veteran midfielder Steed Malbranque said.
Lyon is two points ahead of PSG, having played one game less. PSG lost its second straight home game on Saturday, slipping to an embarrassing 2-1 defeat to Rennes, which played most of the second half with nine players and a third-choice goalkeeper.
At Stade Gerland, Lopez was involved in the first goal, when his clever backheel released fullback Anthony Reveillere down the left and his cross was turned in by Weber.
Malbranque showed why France coach Didier Deschamps considered giving him a call up at the age of 32, playing a part in the next two goals.
In the 73rd, his cross from the right was clumsily hacked away by Grezgorz Krychowiak, the ball hit the crossbar and fell invitingly for Gomis to notch his sixth league goal of the season. Gomis also scored the winner for France in the 2-1 win away to Italy in midweek.
"We are united, we attack and defend together. It's satisfying to keep a clean sheet today," Gomis said. "I was in the right position when the ball fell to me. It shows that I'm in form."
Then, in the last minute, Malbranque got the ball 40 yards out and picked out Lopez with a superb pass, and the Argentine forward beat goalkeeper Kossi Agassa with an assured finish for his fifth of the campaign.
Also, Argentine forward Dario Cvitanich scored in the second half as Nice beat Toulouse 1-0 at home. Nice, which has drawn seven games this season, is in 11th spot.