Mazzarri, on the other hand, was made to suffer as Inter Milan spluttered to a 2-0 win with late goals from Yuto Nagatomo and Rodrigo Palacio at a half-empty San Siro.
Mazzarri, Inter's sixth coach since Jose Mourinho left after completing the treble three years ago, was greeted by a lukewarm atmosphere as he replaced Andrea Stramaccioni who led Inter to a dismal ninth last season, including seven home defeats.
"These boys hadn't won at home for 4-1/2 months, they had to exorcise a psychosis," Mazzarri told Sky Sports Italia.
"We are getting better and we are finding a balance. We are improving more than I had anticipated, we've done a lot in a short space of time."
In other games, AS Roma beat promoted Livorno 2-0 on coach Rudi Garcia's debut while Hernanes and Antonio Candreva, from a penalty, scored in the first 20 minutes to set up a 2-1 win for Lazio over Udinese.
Torino overcame Sassuolo, another promoted side 2-0, while Cagliari beat Atalanta 2-1 and Parma and Chievo played out a goalless stalemate.
Cagliari, unable to find a suitable venue in Sardinia, played their game in Trieste on the border with Slovenia, around 1,000 kilometres from their base.
HIGUAIN DEBUT
There was plenty for Benitez to celebrate at Napoli as Gonzalo Higuain also made an impressive debut following his move from Real Madrid while Pepe Reina in goal was barely tested.
Callejon his the post early on and put Napoli ahead in the 32nd minute from a rebound after Hamsik's shot had been saved.
Higuain had a goal ruled out for offside shortly afterwards before Hamsik scored a brilliant second, slaloming his way through the defence before scoring from a narrow angle despite being off-balance.
Although Napoli slowed after the break, they were still in control and Hamsik turned in Goran Pandev's cross just after the hour for their third.
It was a different story at San Siro where Mazzarri was visibly relieved on the touchline when Rodrigo Palacio sealed victory with Inter's second goal in stoppage time after Yuto Nagatomo had put them ahead with a fortuitous goal.
Mazzarri, Inter's sixth coach since Jose Mourinho left after completing the treble three years ago, was greeted by a lukewarm atmosphere for his first league game since replacing Andrea Stramaccioni who led Inter to a dismal ninth last season.
Inter dominated the game but, with captain Javier Zanetti, defender Walter Samuel and striker Diego Milito still missing with long-term injuries, their play was disjointed and shoddy.
Genoa, playing their first match under new coach Fabio Liverani, offered little threat of their own and Inter finally broke through with 15 minutes left when Jonathan's deflected cross caught their defence offguard and Nagatomo headed in at the far post.
Argentine Mauro Icardi, signed from Sampdoria in the close season, saw his header hit the crossbar shortly afterwards before compatriot Palacio latched on to Fredy Guarin's through ball to slip the ball past Mattia Perin.
(Writing by Brian Homewood in Berne; Editing by John Mehaffey)
