The victory meant joint-fifth Genoa moved within one point of Samp in fourth ahead of Sunday's main programme of games.
Midfielder Omar Milanetto converted a 10th minute penalty after Reto Ziegler tripped Rodrigo Palacio and Genoa almost extended their lead soon after when left back Ziegler deflected a cross onto his own post.
Domenico Criscito then rattled the bar with a header before Genoa team mate Giuseppe Biava naively handled the ball just before the break and was sent off having already been booked.
Despite the dismissal, Gian Piero Gasperini's side continued to dominate and captain Marco Rossi netted early in the second period after a quick counter-attack.
Sampdoria namesake Marco Rossi was then sent off for a second yellow and Genoa's Raffaele Palladino, who angered rival players and fans with his celebration, made it 3-0 from the spot after Ziegler again committed a foul.
Early season leaders Samp, who had not won in three before last weekend's victory over Chievo, struggled throughout with talisman Antonio Cassano unusually quiet and they lost Fabrizio Cacciatore to a straight red for a nasty tackle late on.
The Genoa derby is well-known for its colourful fans and with both clubs doing well in the top half of Serie A, there was an extra party atmosphere at their shared stadium - so much so that the kick-off was delayed because of smoke from fireworks.
In the early match, mid-table Udinese secured a routine 2-0 home win over lowly Livorno thanks to a perfect free-kick from Serie A top scorer Antonio Di Natale and a header from Antonio Floro Flores in the first half.
