Marcelo Bielsa's side have not won on the road in Ligue 1 since October and mid-table Nice's third straight win means Olympique Lyonnais will remain top at the end of the weekend irrespective of Sunday's visit of Metz.
Defender Romain Genevois netted from close range early in the second half after Marseille failed to deal with a free kick into the box but a second yellow card for Kevin Gomis quickly threatened the home team's chances.
Nice, though, went 2-0 up through Niklas Hult's first league goal of the season when he scored unmarked at the back post and although Florian Thauvin pulled one back 13 minutes from time, the Cote d'Azur side were good value for the win.
Second-placed Marseille have 44 points from 22 games, one behind Lyon and three more than faltering champions Paris St Germain who travel to St Etienne on Sunday.
(Writing by Mark Meadows, editing by Tony Jimenez)
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