Grenoble opened the scoring through playmaker Laurent Battles just before half-time but had midfielder Jimmy Juan sent off for a second booking early in the second half.
The visitors then stepped up a gear and took the points courtesy of headed goals from winger Yoan Gouffran and Morocco striker Marouane Chamakh followed by a late strike from Argentine forward Fernando Cavenaghi.
"We knew it would be difficult here and it was," Chamakh told French television Canal Plus after beating Grenoble who have just one victory from 21 games.
Bordeaux looked short of ideas at first but played a lot better after the break.
"We showed a different spirit in the second half," Bordeaux goalkeeper Ulrich Rame said.
"Having a player sent off made it difficult for them and we were able to capitalise on that," he added. "We made the most of the opportunities we had, scoring three times from five shots at goal."
EIGHT CLEAR
The win put Bordeaux on 47 points from 21 games, eight clear of Montpellier, who moved up to second by winning 1-0 at Racing Lens thanks to a goal from Colombian striker Victor Hugo Montano three minutes from time.
Lille, who had won their last seven league matches and scored at least three goals in each, dropped a spot to third, 10 points off the pace, with a 2-1 defeat at lowly Sochaux.
Olympique Marseille, who drew 1-1 at Bordeaux on Sunday, fought back from a goal down to beat struggling Le Mans 2-1 with two goals, including a penalty, from their captain Mamadou Niang.
The former European champions are in fourth place, level on 36 points with fifth-placed Olympique Lyon, who were also a goal down at Lorient but won 3-1 helped by two goals from Sweden midfielder Kim Kallstrom.
"This is very positive, coming after the draw at Bordeaux," Marseille coach Didier Deschamps told reporters. "The championship is still long and things can change fast."
Paris Saint-Germain struggled in front of their own fans, losing 1-0 to Monaco with an own goal from goalkeeper Apoula Edel to stay in 10th place and fall 18 points off the pace.
