The Partenopei had lost to Sampdoria and drawn with Torino in their last two matches and, although they claimed three points at the Stadio Luigi Ferraris, they could not take the Scudetto race down to the final weekend as Juventus picked up the point they needed at Roma.
Samp, with slender hopes of making the Europa League, thought that they were behind just a couple of minutes in as Dries Mertens found the net from a corner but saw the offside flag go up.
Piotr Zielinski also got an attempt on target for Belec to this time punch clear, before Insigne curled his latest shot marginally wide.
Napoli were the side looking the more likely to score the opener, however, with Insigne also skimming the post and testing Belec from close range.
Milik finally gave the visitors a breakthrough soon after coming off the bench, controlling the ball and bending it past Belec into the top corner.
Albiol doubled the Partenopei's advantage with a guided header 10 minutes from time, helping to lift his side up to 88 points for the season.
SAMPDORIA (4-3-1-2): Belec; Bereszynski, Ferrari, Andersen, Regini (Strinic 82'); Linetty, Torreira, Praet; Ramirez; Caprari (Duvan Zapata 69'), Kownacki (Alvarez 87')
NAPOLI (4-3-3): Reina; Hysaj, Albiol, Koulibaly Mario Rui; Allan (Rog 82), Jorginho, Zielinski; Callejon (Hamsik 67), Mertens (Milik 70), Insigne