Maurizio Sarri's side took a 20th-minute lead through Lorenzo Insigne, and held onto that for the reminder of the 90 minutes - despite sustained pressure from the Giallorossi, particularly in the second half.
Pepe Reina made a fantastic save to deny substitute Federico Fazio before the crossbar denied Edin Dzeko, but Roma could not find an equaliser as Napoli made it eight wins from eight in the league.
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Limited by injuries, perhaps Di Francesco's only major selection decision came at centre-back, as Juan Jesus got the nod over Federico Fazio.
Elsewhere both Diego Perotti and Lorenzo Pellegrini returned to the starting lineup after spells out with injury, as Alessandro Florenzi retained his place on the right of a three-man attack.
13' - Corner for Roma. Kolarov's ball beats Reina but Jesus can't get the right contact on his challenge in the air...
15' - Radja's snapshot from the edge of the box is blocked. Good spell of pressure!
19' - Good play from Napoli sees Mertens played through in the box, but Alisson makes a good stop and holds.
20’ - Goal. Napoli lead. The ball falls kindly in the box for Insigne and he slots home. 0-1.
27' - Good work from Bruno Peres sees the ball put into the box - Dzeko wins the header but can't direct it on target.
34' - Alisson saves and holds as Mertens meets the corner.
See more images in our dedicated match gallery.
50' - First half of the chance falls to Dzeko ... but he can't put his shot on target from 25 yards out.
56' - Kolarov goes for goal from 25 yards out but fires wide. At the other end, Mertens shoots wide after Manolas falls.
67' - Good spell from the hosts ends with Pellegrini's low cross being deflected beyond everyone across the six-yard box...
70' - CLOSE! Fazio plants his header on target from a corner but Reina makes an incredible save!
83' - BAR! SO UNLUCKY! Dzeko meets Kolarov's corner but his header glances away off the crossbar with Reina beaten!
89' - The hosts are applying the pressure ... but Napoli escape as Cengiz's cross-shot evades everyone on the way out.
90'+5 - NO! Kolarov swings in one final chance for the hosts ... it reaches Cengiz at the back post but Reina saves!
See more game statistics in our dedicated match centre.
“If you look at the stats, Napoli usually hog possession but we shared it tonight – that shows you how evenly balanced it was. They took the lead from a mistake of ours and it gave them a boost but we didn't do enough to get ourselves back in it.”
- Eusebio Di Francesco
"After the break we showed a good response, we created opportunities but unfortunately the goal did not come. We have to continue to be united as a group, when we win and when we lose."
- Federico Fazio
The Giallorossi now have two big away trips to contend with - as they travel to face Chelsea in the Champions League on Wednesday night, and then Torino in the league on Sunday.
There next home game is the following Wednesday, as Crotone come to the Stadio Olimpico for more Serie A action.
Goalscorers: Insigne (20')
Roma: Alisson; Peres, Manolas (Fazio), J. Jesus, Kolarov; Nainggolan, De Rossi, Pellegrini (Gerson); Florenzi (Cengiz), Dzeko, Perotti.
Napoli: Reina; Hysaj, Albiol, Koulibaly, Ghoulam; Allan, Jorginho, Hamsik; Callejon, Mertens, Insigne.
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