Out-of-form striker Andre-Pierre Gignac broke the deadlock with only his second goal of the season before Brandao doubled the lead in the dying seconds of the first half.
Bordeaux reduced the deficit 15 minutes from time thanks to Anthony Modeste's penalty.
Champions Marseille lie fifth in the standings on 32 points, three adrift of Lille. Bordeaux slipped to 10th on 27 points.
Lille retained their one-point advantage at the top with a 2-0 win at Nice on Saturday as all the leading teams won on their return to action following the three-week winter break.
The Northeners lead on 35 points, just ahead of Paris Saint-Germain, Stade Rennes and Olympique Lyon. At Marseille's Stade Velodrome, Bordeaux made the better start but were punished for defensive errors.
FINE CROSS
In the 23rd minute, the unmarked Gignac poked the ball between the legs of Bordeaux goalkeeper Cedric Carrasso following a fine cross by Taye Taiwo from the left.
Gignac, a 16.5 million euro signing from Toulouse, had only scored one goal in Ligue 1 this season and had been heckled by his own supporters.
A few seconds before the interval, diminutive midfielder Mathieu Valbuena took advantage of a misunderstanding between Carrasso and his defence to set up Brazilian striker Brandao who fired the ball in an empty net.
Bordeaux created more chances in the second half and were rewarded in the 74th minute with a penalty scored by substitute Modeste but Marseille held on to notch up their first victory in six league games.
"It is a good thing to come back to winning ways. It had been a while. We are back on track. It was important to win," Marseille coach Didier Deschamps told French TV channel Canal Plus.
Lille beat Nice 2-0 on Saturday thanks to goals from the league's top scorer Moussa Sow and Gervinho.
