Inter coach Jose Mourinho rotated his line-up and paid the price when Nelson Rivas, playing as an unaccustomed right back, allowed Cassano to steal the ball and chip reserve keeper Francesco Toldo on nine minutes.
Pazzini made the most of more loose Inter defending when he headed in from close range following a corner and the former Fiorentina forward grabbed a second on 42 minutes when the Serie A leaders again failed to clear a ball in the box.
Inter drew 3-3 in the league with AS Roma on Sunday and Mourinho, facing an Italian federation charge for an outburst against his rivals on Tuesday, bemoaned more poor defending.
"It was again a ridiculous first goal," Mourinho told Rai television. "Rivas has not done well -- he knows it, we know it, but on the field we are all together and take responsibility together.
"When not all the players are there and we make changes...the team does not have the same quality," added the Portuguese, who picked his team with one eye on next Wednesday's Champions League match at Manchester United.
Samp lost defender Daniele Gastaldello to a second yellow card on the hour but Inter, bidding to reach their fifth straight final, did not come especially close late on.
The rainswept Genoa night got worse for Inter when striker Mario Balotelli was carried off on a stretcher after collapsing in the middle of the pitch having collided with the post minutes earlier.
Lazio beat Juventus 2-1 at home in Tuesday's semi-final first leg with the second legs taking place in April.
