That goal came after Lazio lost their goalkeeper Federico Marchetti to a red card in the 29th minute, forcing the Biancocelesti to play for an hour with only 10 men.
There were a total of nine yellow cards shown also by the referee, who had a busy night keeping a lid on things as Genoa left with the points to move to within two points of their hosts.
Lazio started brightly and Genoa goalkeeper Mattia Perin was in the thick of the action early on.
He made two excellent saves to deny Lucas Biglia and then Antonio Candreva before Genoa managed to gain a foothold in the game with a flurry of fouls and yellow cards breaking up Lazio’s momentum.
The colour of the next card was red for Marchetti after he was adjudged to have fouled M’Baye Niang inside the penalty area with just under half an hour on the clock.
Danilo Cataldi was sacrificed so that Etrit Berisha could fill the vacant place in goal, but his first task was to pluck the ball out of his own goal as Perotti made no mistake from the spot.
With an extra man, Genoa were finding more spaces, but they were struggling to find the second goal.
Iago Falque failed to beat Berisha in two one-on-one situations early in the second half before Lazio got their second wind and Stefano Mauri was denied only by the post.
Genoa duly retreated, inviting even more pressure from the hosts, who no longer appeared to have one man fewer.
The visitors posed a threat a few times on the counter-attack, but when Marcel Lestienne thought he had doubled their lead, the linesman’s flag was raised, not that it made any difference to the final result.