Earlier, Senegalese striker Khouma Babacar scored twice and set up another goal as Fiorentina beat Sassuolo 3-1 to notch their sixth away win of the season.
Fiorentina occupy fourth position on 38 points, four adrift of third-placed Napoli.
Leaders Juventus (53 points) travel to Cesena on Sunday when second-placed AS Roma (46) host rock bottom Parma.
Palermo took advantage of mistakes from the visitors to chalk up their fifth home win in six games and climb to seventh.
A bad blunder by Napoli goalkeeper Rafael allowed the hosts to go in front in the 14th minute when he let in a 40-metre shot from Moroccan defender Achraf Lazaar that bounced in front of him.
"We allowed a goal that no one was expecting," Benitez told Sky Sports Italia.
"He had been doing really well. Any time a goalie makes a mistake it doesn't go unnoticed."
DYNAMIC DYBALA
Inspirational Argentine Paulo Dybala then laid on Palermo's second and third goals.
Dybala set up Franco Vazquez for a low shot from just outside the box that flew past Rafael after 36 minutes.
"We made another mistake, lost possession and they scored again," Benitez said. "When we fall behind we have to maintain more composure."
Twenty minutes after the break Palermo put the game out of reach for Napoli.
Once again Dybala was given time to find Vazquez with a long pass and from his header, Luca Rigoni tapped the ball in from close range.
New signing Manolo Gabbiadini scored a consolation goal for Napoli with eight minutes remaining.
Vincenzo Montella's Fiorentina dominated the first half against Sassuolo and killed off the game in the space of three minutes.
A backheel by Babacar sent Chelsea loanee Mohamed Salah through to score in the 30th minute.
Babacar then made it 2-0 before wrapping up victory in the 62nd minute when he controlled a David Pizarro pass and calmly shot past Andrea Consigli.
Domenico Berardi headed in for 12th-placed Sassuolo five minutes later.
(Writing by Jacopo Lo Monaco, editing by Tony Jimenez)
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