With possession roughly equal, it was Genoa who created twice the amount of opportunities.
Genoa scored the only goal of the game in the 13th minute after Milan Badelj side-footed Ridgeciano Haps’ cross into an empty net.
Ternana almost had their equaliser after a Francesco Cassata effort from distance curved outside the post.
Mamadou Coulibaly wasted a golden opportunity next.
The midfielder, needing only to beat the goalkeeper, scuffed his shot well wide.
Genoa thought they had doubled their lead through Stefano Sturaro, but he was ruled offside.
Ternana head into the last nine games six points clear of the relegation playoff spots.
Watch Serie B live and exclusive on Il Globo TV