Dries Mertens was the matchwinner for the Partenopei, scoring in the 65th minute of the game with a ferocious effort from just inside the area.
The Campanians had lost three of their previous four meetings with Atalanta, including a Coppa Italia quarter-final on January 2, making this fixture a tense proposition for the tabletoppers.
Indeed, neither side could be separated in the first 45 minutes, the hosts playing a tight, pressing game which limited Napoli's forays into the opposition half.
Napoli improved in the second half and were able to find the breakthrough when a defence-splitting Callejon ball bounced into the path of Mertens, who duly drilled home on the half-volley for his first Serie A goal since October 29.
Marek Hamsik and Marko Rog missed sitters against Atalanta late on, while the former saw an injury-time strike ruled out for offside, but Maurizio Sarri's men still managed to hang on for all three points.
ATALANTA (3-4-1-2): Berisha; Toloi, Caldara, Masiello; Hateboer, Cristante, Freuler, Spinazzola (Gosens 62'); Ilicic (Haas 75'); Cornelius, Gomez
NAPOLI (4-3-3): Reina; Hysaj, Albiol, Koulibaly, Rui; Allan, Jorginho, Zielinski (Rog 86'); Callejon (Maggio 91'), Mertens, Insigne (Hamsik 74')