The champions were top six weeks ago but have dropped to sixth place, lost the League Cup final to Olympique Marseille and suffered Champions League elimination at the hands of Olympique Lyon.
They also lost Yoann Gourcuff through injury on Saturday, with the World Cup-bound France playmaker suffering from a strained thigh muscle. He was replaced at half time.
"Really, tonight, I'm stunned because leaving Lorient without a single point after such a game, it means luck is really not with us," Bordeaux coach Laurent Blanc told French radio Europe 1.
"We don't take a point and we lose another player. This time, it's Gourcuff."
Bordeaux have a game in hand but are four points behind Lille, who moved up to third with four matches left after a 2-1 victory at lowly Le Mans. The third-placed team goes into the Champions League playoffs for next season's competition.
Midfielder Yohan Cabaye hit Lille's winner with a penalty 12 minutes from time after striker Gervinho was brought down.
Le Mans striker Modibo Maiga had struck in the 55th minute to cancel out Tulio De Melo's 13th-minute opener but the visitors kept pushing and deserved victory.
Bordeaux should have taken the lead before half time at seventh-placed Lorient, Alou Diarra fluffing a good early chance and Yoan Gouffran's shot from inside the box hitting the bar.
OFF GUARD
The champions, without influential centre-backs Michael Ciani and Marc Planus, were then caught off guard in the 57th minute.
Lorient striker Gameiro raced past defender Ludovic Sane before firing past Ulrich Rame to score the only goal of a lively game.
Fourth-placed Montpellier, one point behind Lille, had to settle for a goalless draw at mid-table AS Nancy.
Montpellier were denied a last-gasp winner when referee Stephane Bre disallowed Fode Koita's effort for offside. TV replays indicated he was onside.
Lyon are fifth on 59 points, with a game in hand over Lille and Montpellier, after the French League postponed their match against Monaco to allow them to rest for Tuesday's Champions League semi-final return leg at home to Bayern Munich.
Paris Saint-Germain, who will play Monaco in the French Cup final next Saturday, salvaged a 1-1 home draw against Stade Rennes when striker Guillaume Hoarau cancelled out Jerome Leroy's first-half opener in the 64th minute.
