Maxi Lopez's 24th-minute strike gave the Blucerchiati fans bragging rights until the two sides next meeting next season, earning Samp a crucial three points which take them eight points clear of the relegation zone, and up to within two points of their hosts.
The Rossoblu searched in vain for a route back into the game in a one-sided second half, failing to make the breakthrough in wet and muddy conditions.
Sampdoria coach Sinisa Mihajlovic took a gamble on Lopez, who only joined the club last week, and he was repaid when the former Catania forward exchanged passes with Shkodran Mustafi before flashing his shot across Mattia Perin into the left-hand corner.
The official visitors to the Stadio Luigi Ferraris could have had a second when Angelo Palombo's free-kick only just missed the left-hand upright with Perin immobile.
Genoa struggled to match their guests in terms of hunger and desire, but as the first-half wore on, and with their fans trying to lift them, they managed to find a foothold in the game.
Alberto Gilardino tested Angelo Da Costa with a header before Andrea Bertolacci's shot was tipped over the crossbar.
Luca Antonelli did put the ball into the back of the net just before half-time, but the goal was ruled out for offside.
Genoa had another goal ruled out for offside midway through the second half as they camped themselves in the Sampdoria half.
They inevitably left gaps at the back and Lopez almost capitalised on one of them, but Perin was alert to the danger, saving Genoa from further damage, but not enough as Lopez's earlier goal proved the difference between the two sides.