The home side, currently in the lower half of the table, were quick off the starting blocks, with Stefano Sturaro firing wide of the post within the first minute, while two minutes later Marco Motta came close with a header.
An overall lively first half saw end-to-end action with offensive play and chances for both sides, with Diao Keita, Alberto Gilardino, Andrea Bertolacci, Ogenyi Onazi and Stefano Mauri, among others, all weighing in with efforts.
Despite the glut of chances from both teams, the scoreline remained goalless in the first half, but this was to change in the second period, former World Cup winner Gilardino drawing first blood for the home side in the 65th minute.
Shell-shocked Lazio soon found themselves in even more trouble when Giannis Fetfatzidis struck with just seven minutes of regulation time left in the match to put Genoa 2-0 up.
The Biancocelesti's misery was compounded when Cristian Ledesma was sent off after picking up two yellow cards in quick succession at the end of the game.