Jordan Ayew's header in the 54th minute lifted a dominant Marseille to 15 points from five games, two ahead of Olympique Lyon who beat Ajaccio 2-0.
Marseille, who had never previously won their five opening league matches, outclassed their lowly hosts in the first half but lacked sharpness.
"We should have been one, two or three goals ahead at halftime because we had the chances," coach Elie Baup told French channel Canal Plus.
"This is the way I want us to play."
Striker Andre-Pierre Gignac had four clear-cut chances but he either missed the target or was denied by goalkeeper Guy-Roland Ndy Assembe.
Andre Ayew shot past Ndy Assembe in the 11th minute, only to see defender Vincent Muratori stop the ball on the goal line.
Marseille kept creating chances after the break and Ayew eventually put them in front when he netted a powerful header from the penalty spot after his brother Andre's cross.
Nancy tried to mount a comeback without really threatening Marseille and lie 17th in the standings on four points.