Carlos Carmona's early goal consigned Napoli to a second defeat of the Serie A season, as the Partenopei struggled without star striker Edinson Cavani.
Walter Mazzarri's men dropped to third in the league standings as the injured Cavani watched his replacements huff and puff with no end product at the Stadio Atleti Azzurri d'Italia.
Atalanta, who played a perfect tactical game in nullifying the Vesuviani, creep into the top half of the table courtesy of a third home win of the season.
Napoli looked lively in the early exchanges, Marek Hamsik and Goran Pandev combining to tee up Andrea Dossena, who miskicked the ball.
Lorenzo Insigne hit the sweetest of shots on the volley but home keeper Andrea Consigli pushed it away for a corner, before Atalanta took the lead.
With 19 minutes played, German Denis found Carmona just outside the box, the Chilean midfielder volleying the ball past a helpless Morgan de Sanctis.
La Dea had a second goal ruled out just four minutes later, Denis gleefully tapping home only to see the offside flag raised on the touchline.
Denis' cross for Giacomo Bonaventura met Davide Brivido instead, the defender smashing wide, before Hamsik was denied a fine volley at the other end.
Atalanta continued to squeeze their visitors out of possession, but Paolo Cannavaro almost scored from distance, Consigli racing across his goal to block the drive.
The hosts came flying out of the blocks after the break, De Sanctis flailing to repel Riccardo Cazzola's header, but Napoli would bare their teeth once again.
First, Insigne slipped Hamsik through on goal, Consigli making the block, before the former tried his luck from the left side of the area.
Consigli stood firm again, as he did when substitute Giandomenico Mesto took aim from distance.
But the Orobici always looked more likely to grab a second than Napoli were to level the match, with Moralez unlucky not to get on the end of Schelotto's low cross 10 minutes from time.