However, Paris Saint-Germain can leapfrog them with a victory over Montpellier away from home later on Sunday.
© AP Photos
It was all Marseille in the opening exchanges, with Benoit Cheyrou coming close twice with headers in the opening nine minutes.
However, Ospina rose up to the challenge and saved Mathieu Valbuena's spot kick.
Ospina again denied Marseille just a minute later when he kept out Amalfitano's shot from the right side of the Nice box.
Five minutes from time, the visiting goalkeeper was eventually beaten when Andre Ayew headed home Valbuena's cross from close range.
Amalfitano went close to doubling the hosts' advantage in the first minute of the second half, but it was Nice who scored the second goal of the match.
Marseille, though, continued to dominate proceedings as Andre Ayew rattled the Nice crossbar with a left-footed shot from close range in the 68th minute.
Moments later Valbuena made it 2-1 to the hosts at Stade Velodrome when he found the target with his left foot from close range..