Antonio Conte's resurgent side wrapped the match up inside the first half, courtesy of an early Romelu Lukaku goal and a sensational strike by Khvicha Kvaratskhelia.
Belgium striker Lukaku completed a permanent move to Napoli from Chelsea on Thursday, ending a long period of limbo with the Blues.
Kevin De Bruyne was included in Belgium’s squad for next week’s Nations League matches but Romelu Lukaku was omitted after asking for time off to concentrate on getting fit after his move to Napoli, coach Domenico Tedesco announced on Friday.
Napoli have signed Romelu Lukaku from Chelsea, the Serie A club announced on Thursday, ending the Belgium striker's extended period in limbo with the Blues.
Paulo Dybala picked out Lukaku with a clever cross as the Belgium striker headed Roma in front in the fifth minute at the Stadio Olimpico.
Bruno Fernandes and Ricardo Horta netted the goals for Roberto Martinez's Portugal, with Cristiano Ronaldo not on the scoresheet, to end with 10 wins from 10 matches in Group J.
Lukaku grabbed his third goal in five league games for Roma after latching onto a clever pass from Paulo Dybala midway through the first half.
Belgium forward Lukaku rolled in Roma's sixth in the 82nd minute of a dominating performance in which talisman Paulo Dybala also got off the mark for the season with a brace.
Romelu Lukaku completed his season-long loan move to Roma from Chelsea on Wednesday after being welcomed as a hero by supporters.
The visitors had been rocked by a row between new coach Domenico Tedesco and veteran goalkeeper Thibaut Courtois in the build-up to the game, and made a slow start before Lukaku pounced with two close-range finishes towards the end of the first half
Thierry Henry said that it will be difficult for Romelu Lukaku to handle after he made some crucial mistakes in Inter's Champions League final loss against Manchester City.
Lukaku, on loan at Inter from Chelsea, has struggled with injuries and form this season, but has scored three goals in his last three games
A Romelu Lukaku brace on his 30th birthday, a further strike from Lautaro Martinez and an unfortunate Ruan Tressoldi own goal were enough for Inter to claim a seventh straight win in all competitions and move level on 66 points with second-placed Juventus
Romelu Lukaku shot Inter Milan to a 3-0 win over struggling Empoli on Sunday with his first Serie A goals from open play since the opening day of what has been a difficult return season in Italy.
Lukaku, who was sent off in the first leg of the semi-final, will remain suspended for the return against Juventus on Wednesday after the club's appeal was rejected by Italy's Sports Court Of Appeal
The Belgian missed clear scoring opportunities during the club's 1-0 defeat by Fiorentina and 1-1 draw with lowly Salernitana over the past 10 days in Serie A, costing the team crucial points in their bid to secure a top four finish
Juventus have been ordered to close part of their stadium for their next home Serie A match against Napoli by an Italian sports judge after Inter Milan striker Romelu Lukaku was racially abused during Tuesday's Coppa Italia semi-final.
Lukaku struck as Sergio Conceicao's Porto were playing the final portion of the match with 10 men after midfielder Otavio was sent off in the 78th minute for his second bookable offence.
Simone Inzaghi's side stay second and are three points ahead of local rivals AC Milan, who beat Monza 1-0 earlier on Saturday, but are a long way behind rampant Napoli after their 2-0 win at Sassuolo on Friday.