Edinson Cavani's second-half penalty earned Napoli a deserved victory in a match they dominated at the Stadio Luigi Ferraris.
The Uruguay international converted after a foul which earned Daniele Gastaldello a red card and Napoli, already the better side against 11 men, could easily have won by more but for wayward finishing throughout.
Samp's Marcelo Estigarribia and Eder had gone close in the first half but they were isolated threats as the home side were largely overrun.
Goran Pandev set the tone early on with a shot which was saved by Sergio Romero, before Christian Maggio and Marek Hamsik failed to test the home goalkeeper.
Estigarribia's shot was just inches wide of the left post and Gastaldello headed over as the Genoese side tried to establish themselves in the game.
Cavani headed just wide and Eder was narrowly off-target at the other end as the first half ended goalless.
Eder's 30-yard effort caused concern for Napoli early in the second period but the visitors were soon back on the offensive, though Hamsik and Hugo Campagnaro were wasteful with their finishing.
The breakthrough came in the 67th minute, though, when Gastaldello brought down Hamsik and was dismissed and Cavani took full advantage by stroking the penalty into the bottom right corner.
From that point on there was only one team in the game, and Romero was forced to take off to save substitute Lorenzo Insigne's shot.
He made an even better save as Cavani targeted the top corner, before Hamsik sliced his shot a long way wide.
Campagnaro had the final chance deep into stoppage time, but blazed his right-foot shot high over the bar.