Lyon end losing streak
The result allowed Lyon to go ten points clear of Grenoble who occupy the first of the two relegation spots and 12 clear of rock-bottom Bayonne.
"It wasn't all perfect but bravo to the players," said Lyon boss Pierre Mignoni.
"Bordeaux gave us a lot of problems in the breakdown and prevented us from getting some dynamism into our game.
"We have ended our four-game losing run. We have never given up but the players needed to rediscover their confidence,"
A drab first half saw the teams locked at 3-3 at the interval after Frederic Michalak, making just his fifth start of the season at scrumhalf, had cancelled out Simon Hickey's early penalty for Bordeaux.
Hickey and Michalak exchanged penalties again early in the second period before Lyon opened a 13-6 lead after 50 minutes with the first try of the game.
Bordeaux's Australian wing Adam Ashley-Cooper was deceived by the bounce from Lyon flyhalf Mike Harris's kick-ahead which allowed wing Toby Arnold to score. Michalak kicked the extras.
Bordeaux's Irish replacement flyhalf Ian Madigan cut the deficit to 13-9 with a penalty before Michalak and Jacques-Louis Potgieter, with a monster 40m kick, put Lyon back in charge at 19-9.
Replacement scrumhalf Yann Lesgourgues scored Bordeaux's lone try in the last minute with Madigan converting for 19-16.
It came too late to save play-off hopefuls Bordeaux but it did give them a losing bonus point as they remained in sixth spot in the table.
Agence France-Presse