Replacement keeper Etrit Berisha's first act was to pick the ball out of his net after Diego Perotti coolly slotted the penalty into the bottom right corner.
Genoa should have sealed the match early in the second half when Niang sent Iago Falque clear on goal, but the Spaniard fired narrowly past the right upright.
It was almost made to rue its missed opportunities as Lazio went close to leveling when Stefano Mauri was sent through by Miroslav Klose, but the captain hit the right post.
"We played well but we weren't very clinical and in the future we need to be if we want to remain up there," Genoa coach Giampiero Gasperini said. "It was an important win after picking up so few points in the last few matches."