The Mediterranean derby was decided when Marseille defender Leonardo Balerdi was sent off for a second yellow card and substitute Evann Guessand headed in the resulting free-kick in the 79th minute.
Nice 1-0 Marseille - Highlights
The result maintained Nice's unbeaten record this season under 34-year-old Italian coach Francesco Farioli and left them top, although Cote d'Azur rivals Monaco will replace them at the summit by beating Metz on Sunday.
Nice have enjoyed a fine start to the season despite British owner Jim Ratcliffe being focused on acquiring a stake in Manchester United.
Marseille have won only once in four games under new coach Gennaro Gattuso and are seven points behind the leaders.
