The former Liverpool and Chelsea manager has been tasked with beating Juventus to the Scudetto and his new-look side fired an early warning shot to the reigning champions.
Summer signing Jose Callejon scored a debut goal after dazzling with his skills in the first half and fan favourite Marek Hamsik made sure of the points with goals either side of half-time.
Bologna, who beat Napoli twice last season, were all at sea and enjoyed one tangible chance through Panagiotis Kone late on.
Four of Benitez's new recruits - Gonzalo Higuain, Raul Albiol, Pepe Reina and Callejon - started in Naples and the latter smashed the ball off a post with Gianluca Curci beaten in the sixth minute.
The former Real Madrid winger then found Hamsik free inside the area, but the Slovakian's header was easily claimed by Curci.
Callejon continued to menace the visitors and in the 21st minute he sent Higuain through on goal, only for the Argentinian striker to lose control of the ball near the penalty spot.
When the opening goal arrived in the 32nd minute it was no surprise who had made the breakthrough, as Callejon gladly converted a parried long-range sighter from Hamsik.
Higuain thought he had opened his account in Azzurro colours five minutes before the break but, after a swift exchange of passes involving Gokhan Inler and Hamsik, the offside flag went up as he beat Curci.
Napoli made amends before heading down the tunnel, though, as the skilful Hamsik received the ball on the left before skipping over Gyorgy Garics to clip home a second two minutes into stoppage time.
Moments after the restart Callejon came sniffing for a third goal of the night and his brace when put through by former Madrid colleague Higuain, only for Curci to push the ball away.
And when Juan Zuniga won a free-kick in a central position, Curci watched Higuain's powerful drive bounce off his left-hand post.
Napoli would not wait long to pull further clear, however, as Hamsik completed his brace courtesy of a defensive mix-up in the Bologna box.
Goran Pandev worked hard to retrieve the loose ball before supplying Hamsik for an easy finish over Curci's shoulders.
The Slovakian received a standing ovation when he was withdrawn for winger Dries Mertens, another Benitez signing, in the 72nd minute.
Bologna had barely left their own half but, when Kone unleashed a fizzing drive from distance, Reina struggled to repel the swinging ball.
Higuain had fallen foul of the flag in the first half and Mertens was similarly denied a debut goal, and a fourth on the night, when tucking home the former's pass from an offside position on 80 minutes.