Bergamo has been an inhospitable venue for Napoli over recent years and a brace from German Denis preceded Maxi Moralez's late goal to condemn the southerners to a fifth defeat from their last eight league games here.
More pressing than the fact Jose Reina, Gokhan Inler and Federico Fernandez each made glaring errors to facilitate Atalanta's goals is the fact that Napoli missed an opportunity to catch up with league leaders Juventus and second-placed Roma, who are eight and six points better off respectively.
Roma might have extended that advantage had their meeting with Parma not been abandoned after only eight minutes of rain-affected play.
There was doubt the league game at Rome's Stadio Olimpico would go ahead at all on Sunday due to incessant heavy rain affecting the Italian capital and kick-off was delayed for several minutes.
Only eight minutes of play took place before referee Andrea De Marco decided to suspend the game for 30 minutes, pending a pitch inspection, but the match was soon officially abandoned following the interruption.
Keita Balde inspired Lazio to a 2-0 win at Chievo which even saw the home fans acknowledging the brilliance of the former Barcelona youth player.
The 18-year-old caused Chievo's defenders a whole host of problems before getting his name on the scoresheet in the second half to seal all three points after Antonio Candreva's early opener.
Alberto Malesani failed to make a winning start as Sassuolo coach as Hellas Verona claimed a 2-1 victory at the Stadio Citta del Tricolore.
Malesani's first assignment since replacing Eusebio Di Francesco in the Sassuolo dugout was a game against his hometown club Verona, who also won automatic promotion from Serie B last season.
Thomas Manfredini made life difficult for the relegation-threatened Neroverde with an own-goal in the 50th minute before veteran striker Luca Toni doubled Verona's lead four minutes from full-time.
Antonio Floro Flores scored a late consolation for Malesani's men but they remain a point from safety ahead of next weekend's daunting trip to Inter Milan.
Serie A strugglers Catania and Livorno shared six goals in a survival thriller at the Stadio Massimino.
Livorno took the lead three times, but were pegged back each time by a courageous Catania, who almost snatched victory in stoppage time of the 3-3 draw.
Innocent Emeghara scored two for Livorno and earned a penalty, which was converted by Paulinho.
Gonzalo Bergessio, Pablo Barrientos and Sergio Almiron replied for the hosts, earning them a point which does not help either side much in their respective battles against the drop.