Lyon have 57 points from 31 matches, one ahead of Bordeaux who dropped to third but have two games in hand.
Bordeaux also trail Lyon 3-1 going into their midweek Champions League quarter-final second leg.
"We didn't get a lot of positive signals before Wednesday's game. We were mediocre at too many aspects of the game," Bordeaux coach Laurent Blanc told reporters after his side suffered their third defeat in a row.
"Too many guys were below par."
Montpellier, on the same points as Lyon, are second on goal difference after being held 0-0 at home by Monaco.
Goalkeeper Stephane Ruffier came to the rescue for Monaco with a string of fine saves.
Auxerre, fourth on 56 points, host Paris St Germain on Sunday and can go top with a win.
PUEL PRAISE
"Hats off to my players who were very strong," said Lyon coach Claude Puel. "But my joy has already gone and I'm already focused on Wednesday's game."
Rennes opened the scoring in the 14th minute when Ghana striker Asamoah Gyan capitalised after Jimmy Briand's shot bounced back off a post.
Michel Bastos put Lyon level when he sent a powerful left-foot shot into the top corner just after the interval. Lisandro Lopez then headed the winner from an Ederson cross in the 61st minute.
Bordeaux dominated possession against Nancy but relied mainly on set pieces after Youssouf Hadji volleyed the visitors in front from a cross by Issiar Dia.
Fernando Cavenaghi tapped in Bordeaux's equaliser from an Alou Diarra header before Dia, who grabbed a hat-trick last week, gained maximum points for Nancy when he scored after running from his own half in the 71st minute.
Bottom club Grenoble and second from bottom Le Mans moved closer to relegation.
Grenoble were beaten 2-1 by Lorient while Le Mans lost 2-0 at fourth from bottom St Etienne.
