Marcelo Bielsa's men had slipped to second after Paris Saint-Germain triumphed 3-2 at Metz on Friday, and they looked set to remain in that position when Thomas Toure slotted beyond goalkeeper Steve Mandanda after 55 minutes.
Mario Lemina rose highest on the hour mark to head Marseille level, but it was not until the final five minutes of regulation time that the hosts assumed the lead at Stade Velodrome.
Andre-Pierre Gignac beat Cedric Carasso with another headed effort from a Dimitri Payet delivery, before substitute Michy Batshuayi capitalised on some statuesque Bordeaux defending to fire home his first Ligue 1 goal following a parry from the goalkeeper.
The victory sees Marseille return to winning ways following the defeat to PSG last time out, and re-establishes their one-point advantage over Laurent Blanc's men.
Nantes and Saint-Etienne lost ground on the leading pack as they played out a goalless draw at Stade de la Beaujoire.
Kevin Monnet-Paquet hit the post hit the post midway through the first half for Saint-Etienne, before goalkeeper Remy Riou helped preserve Nantes' 10-match unbeaten run in all competitions by tipping over a Max Gradel strike two minutes from time.
In the day's remaining fixture, Montpellier went ninth with a 2-0 triumph over Toulouse.
Anthony Mounier benefited from a poor Toulouse clearance to send in a half-volley eight minutes before the break, and the points were in the bag when Souleymane Camara fired a low effort beyond Ali Ahamada in the visitors' net.
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