Gignac headed home a Mathieu Valbuena corner kick in the 15th minute, which was enough to secure the win and lift Marseille to 54 points from 30 games. They hold a one-point lead over Lyon who host strugglers Sochaux in the day's late kick-off.
Marseille's eighth away win of the season took them a step closer to Champions League qualification as they are four points above fourth-ranked St Etienne.
Nice are sixth on 48 and are a point adrift of Lille, who won 2-1 at Stade Brest.
"We have been criticised but we have shown the same quality since the season started," OM coach Elie Baup told French channel beIN Sport.
"There are still eight games left and we will have to fight hard to stay on the podium."
It was not all good news for Marseille, however, as key centre back Nicolas Nkoulou had to leave the pitch in the second half with a thigh problem.
"I'll undergo some tests tomorrow," the Cameroon defender said.
The visiting team took advantage of their first chance after a tense opening 15 minutes during which the referee had to break up an on-pitch clash between Nkoulou and striker Dario Cvitanich.
Gignac wasted two further scoring chances and although the home team piled on the pressure throughout the second half, they slumped to their third defeat in four games.
Florian Raspentino put Brest ahead in the 10th minute but their lead was short-lived as Salomon Kalou equalised seven minutes later with a header.
The visitors barely threatened Brest, who have not won any of their last nine home games, until Nolan Roux sealed victory for the 2011 champions with 12 minutes to go.