Francesco Guidolin's men were surprisingly outclassed by the hosts, who move back to the upper echelons after they ended their opponents unbeaten start to the season
First-half goals from Ezequiel Lavezzi and Christian Maggio ensured Walter Mazzarri's outfit halted its three-match winless run, as the visitors appeared to sorely miss talisman Antonio Di Natale in attack, ragged at times despite the misgiving scoreline.
Indeed, it was the home side who dominated the early part of proceedings, with a continuous barrage of Neapolitan snapshots forcing Samir Handanovic into frequent action. Marek Hamsik appeared to have broken the deadlock just 10 minutes in, climbing highest to nod in Lavezzi's free-kick, but it was adjudged to have been taken too early.
Nonetheless, Napoli's early pressure was aptly rewarded as Lavezzi gave his side the lead on 20 minutes, collecting Edinson Cavani's inch-perfect lob pass over the Udinese backline and firing a splendid volley first-time in the box past the Slovenia No.1.
However, Francesco Guidolin's men had a momentary respite, as Kwadwo Asamoah had a pair of powerful long-range strikes to force Morgan De Sanctis into pulling top-drawer stops.
It was only to be a temporary development though, as minutes before the break, Maggio met Blerim Dzemaili's pinpoint cross from the left-hand side with his head to make it 2-0, finishing the half convincingly.
The second half was a far more settled affair, as Napoli seemed content with its winning position. Udinese, however, was desperate to salvage a result, with the arrival of Diego Fabbrini at halftime a sign of its intentions.
However, the likes of Emmanuel Agyemang-Badu and Giampiero Pinzi were heavily exposed to the free-flowing nature of Napoli's high-octane midfield, who continued to dictate the tempo of game and contain the visitors.
Juan Zuniga, a second-half substitute for Napoli, almost claimed a third midway through the half, after the ball fell to him via a defensive mistake from the visitors, but he couldn't find the finish despite the goal at his mercy, as Napoli now climbs to fourth in Serie A, while Udinese's unbeaten start is now over.