Adel Taarabt gave the Rossoneri an early 1-0 lead, but the Partenopei responded well as a Gokhan Inler wonder strike and a Gonzalo Higuain were enough to give Napoli the victory at the Stadio San Paolo.
De Laurentiis used social networking to comment on the win as well as the midweek Coppa Italia match against Roma.
“A great victory! Now all set to wait for Roma,” De Laurentiis said on Twitter.
Napoli lost the first leg of the tie at the Stadio Olimpico, but were able to grab two valuable away goals in the 3-2 loss.
The Giallorossi meanwhile will be coming off a Derby della Capitale clash against Lazio on Sunday.