The Argentine attacker scored twice before setting up Maxi Moralez for a third as the Viola suffered a devastating defeat in Bergamo.
The Partenopei could have moved six points clear of Fiorentina in the race for a Champions League place but fell behind in Bergamo to a goal from German Denis two minutes after the break.
The forward struck again shortly after the hour mark before then setting up Maxi Moralez to seal victory for Atalanta.
With Gonzalo Higuain restricted to the role of substitute, Napoli looked desperately toothless in attack throughout.
Indeed, a wayward Dries Mertens strike aside, Rafael Benitez's men did not threaten the Atalanta goal during the first half.
The hosts fared little better, with an off-target Giacomo Bonaventura header the best they could muster during a dreadful first half.
However, Atalanta hit the front just after the break when Jose Reina allowed a Denis strike from the edge of the area to squirm under him.
Napoli tried to rally but la Dea doubled the advantage on 64 minutes, Denis volleying home emphatically after controlling a disastrous attempted clearance from Gokhan Inler on his knee.
Napoli was still coming to terms with that calamity when Denis flicked the ball on for Moralez, who took full advantage of an untimely slip from Federico Fernandez by coolly slotting the ball past Reina.
Higuain called Andrea Consigli into action soon after, but there was to be no way back for Napoli, which remains third, three points ahead of fourth-placed Fiorentina.