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."
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.