Khvicha Kvaratskhelia and Amir Rrahmani both scored in the second half.
Napoli were looking to bounce back from losing to Lazio last weekend, their second league loss.
They play Eintracht Frankfurt in the Champions League last 16 on Wednesday, leading 2-0 from the first leg, but coach Luciano Spalletti opted not to rotate his squad.
Napoli dominated and almost broke the deadlock in spectacular fashion at the start of the second half, but Victor Osimhen's overhead kick was straight at Atalanta goalkeeper Juan Musso.
Instead, Kvaratskhelia scored an impressive opener on the hour mark when he collected the ball from Osimhen and weaved his way into the area, twisting and turning between defenders, before blasting into the roof of the net.
Rrahmani all but sealed the win in the 77th when he headed a corner into the far bottom corner.
AAP